# A Dynamic Model of Aggregate Demand and Aggregate Supply

PART V Topics in Macroeconomic Theory A Dynamic Model of Aggregate Demand and Aggregate Supply Chapter 15 of Macroeconomics, 8th edition, by N. Gregory Mankiw ECO62 Udayan Roy Inflation and dynamics in the short run So far, to analyze the short run we have used the Keynesian Cross theory, and the IS-LM theory Both theories are silent about Inflation, and Dynamics This chapter presents a dynamic short-run theory of output, inflation, and interest rates. This is the model of dynamic aggregate demand and dynamic aggregate supply (DAD-DAS) Introduction The dynamic model of aggregate demand and aggregate supply (DAD-DAS) determines both real GDP (Y), and the inflation rate ())

This theory is dynamic in the sense that the outcome in one period affects the outcome in the next period like the Solow-Swan model, but for the short run Introduction Instead of representing monetary policy by an exogenous money supply, the central bank will now be seen as following a monetary policy rule The central banks monetary policy rule adjusts interest rates automatically when output or inflation are not where they should be. Introduction The DAD-DAS model is built on the following concepts: the IS curve, which negatively relates the real interest rate (r) and demand for goods and services (Y), the Phillips curve, which relates inflation ()) to the gap between output and its natural level (), expected inflation (E)), and supply shocks (),), adaptive expectations, which is a simple model of expected inflation, the Fisher effect, and the monetary policy rule of the central bank.

Keeping track of time The subscript t denotes a time period, e.g. Yt = real GDP in period t Yt 1 = real GDP in period t 1 Yt + 1 = real GDP in period t + 1 We can think of time periods as years. E.g., if t = 2008, then Yt = Y2008 = real GDP in 2008 Yt 1 = Y2007 = real GDP in 2007 Yt + 1 = Y2009 = real GDP in 2009 The models elements The model has five equations and five endogenous variables: output, inflation, the real interest rate, the nominal interest rate, and expected inflation. The first equation is for output DAD-DAS: 5 Equations

Demand Equation Fisher Equation Phillips Curve Adaptive Expectations Monetary Policy Rule The Demand Equation Natural (or long-run or potential) Real GDP Real interest rate Natural (or long-run) Real interest rate Yt Yt (rt ) t Real GDP Parameter representing the

response of demand to the real interest rates Demand shock, represents changes in G, T, C0, and I0 The Demand Equation Assumption: > 0; although the real interest rate can be negative, in the long run people will not lend their resources to others without a positive return. This is the long-run real interest rate we had calculated in Ch. 3 Yt Yt (rt ) t >0 Assumption: There is a negative relation between output (Yt) and interest rate (rt). The justification is the same as for the IS curve of Ch. 11 Positive when C0, I0, or G is higher than usual or T is lower than usual.

IS Curve = Demand Equation This graph is from Ch. 11 Assume the IS curve is a straight line Then, for any pair of pointsA and B, or C and Bthe slope must be the same r A rt B IS Yt Y

r C rt B IS Yt Y IS Curve = Demand Equation Then, for any point (rt, Yt) on the line, we get , a constant. r rt

IS Yt Y r rt The long-run real equilibrium interest rate of Figure 3-8 in Ch. 3 is now denoted by the lower-case Greek letter . IS Yt Y IS Curve = Demand Equation Now, we also saw in Ch. 12 that the IS curve can shift when there are changes in C0, I0, G, and T

To represent all these shift factors, we add the random demand shock, t. Therefore, the IS curve of Ch. 12 gives us this chapters demand equation IS Curve = Demand Equation rt rt Yt Yt (rt ) t IS Demand Yt The IS curve can simply be renamed the Demand Equation curve

Yt Demand Equation Curve Yt Yt (rt ) t rt Note that if increases (decreases) by some amount, the Demand equation curve shifts right (left) by the same amount. Demand + Yt Note also that if increases (decreases) by some amount, the Demand equation curve shifts up (down) by the same amount. DAD-DAS: 5 Equations

Demand Equation Fisher Equation Phillips Curve Adaptive Expectations Monetary Policy Rule The Real Interest Rate: The Fisher Equation ex ante (i.e. expected) real interest rate rt it Et t 1 nominal interest rate expected inflation rate Assumption: The real interest rate is the inflation-adjusted interest rate. To adjust the nominal interest rate for inflation, one

must simply subtract the expected inflation rate during the duration of the loan. + + = The Real Interest Rate: The Fisher Equation ex ante (i.e. expected) real interest rate rt it Et t 1 nominal interest rate expected inflation rate t 1 increase in price level from period t to t +1, not known in period t Et t 1 expectation, formed in period t, of inflation from t to t +1 We saw this before in Ch. 5

DAD-DAS: 5 Equations Demand Equation Fisher Equation Phillips Curve Adaptive Expectations Monetary Policy Rule Inflation: The Phillips Curve t Et 1 t (Yt Yt ) t current inflation previously expected inflation 0 indicates how much inflation responds when output fluctuates around its natural level

supply shock, random and zero on average Phillips Curve t Et 1 t Yt Yt t Assumption: At any particular time, inflation would be high if people in the past were expecting it to be high current demand is high (relative to natural GDP) there is a high inflation shock. That is, if prices are rising rapidly for some exogenous reason such as scarcity of imported oil or drought-caused scarcity of food Phillips Curve t Et 1 t Yt Yt t Momentum inflation Demandpull inflation Cost-push inflation

This Phillips Curve can be seen as summarizing three reasons for inflation DAD-DAS: 5 Equations Demand Equation Fisher Equation Phillips Curve Adaptive Expectations Monetary Policy Rule Expected Inflation: Adaptive Expectations Et t 1 t Assumption: Assumption: people people expect expect prices prices to to continue continue rising

rising at at the the current current inflation inflation rate. rate. Examples: E2000)2001 = )2000; E2013)2014 = )2013; etc. DAD-DAS: 5 Equations Demand Equation Fisher Equation Phillips Curve Adaptive Expectations Monetary Policy Rule Monetary Policy Rule The fifth and final main assumption of the DAD-DAS theory is that The central bank sets the nominal interest rate and, in setting the nominal interest rate, the

central bank is guided by a very specific formula called the monetary policy rule Monetary Policy Rule Current inflation rate Parameter that measures how strongly the central bank responds to the inflation gap Parameter that measures how strongly the central bank responds to the GDP gap it t t Y Yt Yt Nominal

interest rate, set each period by the central bank Natural real interest rate * t Inflation Gap: The excess of current inflation over the central banks inflation target GDP Gap: The excess of current GDP over natural GDP Example: The Taylor Rule Economist John Taylor proposed a monetary policy rule very similar to ours:

iff = + 2 + 0.5 ( 2) 0.5 (GDP gap) where iff = nominal federal funds rate target YY GDP gap = 100 x Y = percent by which real GDP is below its natural rate The Taylor Rule matches Fed policy fairly well. CASE STUDY 10 Percent 9 8 7 The Taylor Rule actual Federal Funds rate 6 5

4 3 2 1 Taylors rule 0 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 SUMMARY OF THE DADDAS MODEL The models variables and parameters Endogenous variables: Yt Output t Inflation rt Real interest rate it Nominal interest rate Et t 1 Expected inflation The models variables and parameters

Exogenous variables: Yt Natural level of output * t Central banks target inflation rate t Demand shock t Supply shock Predetermined variable: t 1 Previous periods inflation The models variables and parameters Parameters: Responsiveness of demand to the real interest rate Natural rate of interest Responsiveness of inflation to output in the Phillips Curve Responsiveness of i to inflation in the monetary-policy rule Y Responsiveness of i to output in the monetary-policy rule The DAD-DAS Equations

Yt Yt (rt ) t Demand Equation rt it Et t 1 Fisher Equation t Et 1 t Yt Yt t Et t 1 t Phillips Curve Adaptive Expectations it t t Y Yt Yt * t Monetary Policy Rule DYNAMIC AGGREGATE SUPPLY Recap: Dynamic Aggregate Supply

t Et 1 t Yt Yt t Phillips Curve Et t 1 t Adaptive Expectations Et 1 t t 1 t t 1 Yt Yt t DAS Curve The Dynamic Aggregate Supply Curve t t 1 Yt Yt t t DAS DAS slopes slopes upward: upward: high high levels levels of of output output are are associated associated with

with high high inflation. inflation. This This is is because because of of demanddemandpull pull inflation inflation DASt t 1 t Yt Yt The Dynamic Aggregate Supply Curve t t 1 (Yt Yt ) t DAS2011 2010 2011

Y2011 If you know (a) the natural GDP at a particular date, (b) the inflation shock at that date, and (c) the previous periods inflation, you can figure out Ythe location of the DAS curve at that date. The Dynamic Aggregate Supply Curve t t 1 (Yt Yt ) t DAS2015 2014 2015 Dont forget this: when , the height of the DAS curve is

always . That is, when the economy is at full employment, the height of the DAS curve is inherited inflation plus the current supply shock. Y2015 Y Shifts of the DAS Curve t t 1 (Yt Yt ) t Any Any increase increase (decrease) (decrease) in in the the previous previous periods

periods inflation inflation or or in in the the current current periods periods inflation inflation shock shock shifts shifts the the DAS DAS curve curve up up (down) (down) by by the the same same amount amount DASt

t 1 t Yt Y Shifts of the DAS Curve t t 1 (Yt Yt ) t DASt t 1 t Yt Y Any Any increase increase (decrease) (decrease) in in the the previous previous periods

periods inflation inflation or or in in the the current current periods periods inflation inflation shock shock shifts shifts the the DAS DAS curve curve up up (down) (down) by by the the same same Any Any increase increase amount

amount (decrease) (decrease) in in natural natural GDP GDP shifts shifts the the DAS DAS curve curve right right (left) (left) by by the the exact exact amount amount of of the the change. change. The DAS Curve: Summary The DAS curve is upward sloping When the economy is at full employment, the

height of the DAS curve equals inherited inflation plus the current supply shock When either the previous periods inflation or the current periods inflation shock increases (decreases), the DAS curve shifts up (down) by the same amount When natural GDP increases (decreases), the DAS curve shifts right (left) by the same amount Buckle up for some tedious algebra! DYNAMIC AGGREGATE DEMAND The Dynamic Aggregate Demand Curve The Demand Equation t Y Yt (rt ) t rt it Et t 1 Yt Yt ( it Et t 1 ) t

Yt Yt ( it t ) t Fisher Fisher equation equation Et t 1 t adaptive adaptive expectation expectation ss The Dynamic Aggregate Demand Curve it t t Y Yt Yt Yt Yt ( it t ) t * t

monetary monetary policy policy rule rule Yt Yt [ t ( t t* ) Y (Yt Yt ) t ] t Yt Yt [ ( t t* ) Y (Yt Yt )] t Were almost Dynamic Aggregate Demand Yt Yt [ ( t t* ) Y (Yt Yt )] t * t Yt Yt ( t ) Y Yt Y Yt t * t Yt Y Yt Yt ( t ) Y Yt t (1 Y ) Yt (1 Y ) Yt ( t t* ) t

1 * Yt Yt ( t t ) t 1 Y 1 Y Yt Yt A ( t t* ) B t This is the equation of the DAD curve! The Dynamic Aggregate Demand Curve ( = ) + DAD

DAD slopes slopes downward: downward: When When inflation inflation rises, rises, the the central central bank bank raises raises the the real real interest interest rate, rate, reducing reducing the the demand demand for for goods goods and and services. services. DADt

Y Note that the DAD equation has no dynamics in it: it only shows how simultaneously measured variables are related to each other The Dynamic Aggregate Demand Curve ( = t* DADtB Yt B t Y

) + The Dynamic Aggregate Demand Curve ( = ) + When the central banks target inflation rate increases (decreases) the DAD curve moves up (down) by the exact same amount. t* Note how monetary policy is described in terms of the target inflation rate in the DAD-DAS model DADt2

DADt1 Yt B t Y Monetary Policy In the IS-LM model, monetary policy was described by the money supply or the interest rate Expansionary monetary policy meant M or i Contractionary monetary policy meant M or i In the DAD-DAS model, Expansionary monetary policy is * Contractionary monetary policy is * The Dynamic Aggregate Demand Curve ( = ) +

t* DADt2 DADt1 Yt B t When the natural rate of output increases (decreases) the DAD curve moves right (left) by the exact same amount. When there is a positive (negative) demand shock the DAD curve moves right (left) . Y A positive demand shock could be an increase in C0, I0, or G, or a decrease in T. The Dynamic Aggregate Demand Curve (

= ) + DADt2 DADt1 The The DAD DAD curve curve shifts shifts right right or or up up if: if: 1. 1. the the central central banks

banks target target inflation inflation rate rate goes goes up, up, 2. 2. there there is is aa positive positive demand demand shock, shock, or or 3. 3. the the natural natural rate rate of of output output increases. increases. Y

The DAD Curve: Summary The DAD curve is downward sloping When the central banks target inflation rate increases (decreases), the DAD curve shifts up (down) by the same amount When natural GDP increases (decreases), the DAD curve shifts right (left) by the same amount When the demand shock increases (decreases), the DAD curve shifts right (left) SUMMARY: DAS AND DAD EQUATIONS Summary: DAS and DAD Equations DA S DA D t t 1 Yt Yt t 1 *

Yt Yt ( t t ) t 1 Y 1 Y Note that there are two endogenous variablesYt and tin these two equations Therefore, we can solve for the equilibrium values of Yt and t The Solution! Using the equations in the previous slideand a lot of very tedious algebra one can express output and inflation entirely in terms of exogenous variables, parameters, shocks and pre-determined inflation. This is the algebraic solution of the DAD-DAS model. The Solution! And once we solve for the equilibrium values of Yt and t, we can use adaptive expectations to solve for expected inflation: . We can use the monetary policy rule to determine the nominal interest rate and the Fisher Effect to solve for the real interest rate

The Solution! By substituting the previous slides solutions for output and inflation into the monetary policy rule, we can then get the above solution for the nominal interest rate. The Fisher equation can be used to solve for the real interest rate. Please do not worry about the solution and its derivation. However, if you are interested, please see http://myweb.liu.edu/~uroy/eco62/ppt/zlb-educ130328.pdf , especially sections 4.1 , 8.1 (appendix) and 8.2 (appendix). Summary: DAD-DAS Slopes and Shifts DAS Upward sloping If natural output increases, DAS shifts right by same amount If previous-period inflation increases, DAS shifts up by same amount If inflation shock increases, DAS shifts up by same amount DAD Downward sloping

If natural output increases, DAD shifts right by same amount If target inflation increases, DAD shifts up by same amount If demand shock increases, DAD shifts right EQUILIBRIUM: SHORT-RUN AND LONG-RUN Short-Run Equilibria The economy is in short-run equilibrium at time t if output and inflation are at the intersection of the DAD and DAS curves for time t.

DAS2004 D 2004 DAD2004 Y2004 Y Short-Run Equilibria Any increase in the natural output () shifts both curves right by the same amount. This raises output by the same amount and leaves 2004 inflation unchanged. DAS2004 D DAS2004* D*

DAD2004* DAD2004 Y2004 Y Short-Run Equilibria Any increase in the previous periods inflation (t-1) or the current inflation shock (t) will reduce output and raise 2004 inflation right away (stagflation). DAS2004* D* DAS2004 D DAD2004 Y2004

Y Short-Run Equilibria Any increase in the central banks inflation target (*) or the demand shock (t) will raise both output and inflation 2004 right away. DAS2004 D* D DAD2004* DAD2004 Y2004 Y Short-Run Equilibria DAD-DAS Predictions, Short-Run

Current inflation in one year becomes past inflation in the next year. Yt t + 0 * + + t + + t

+ t-1 + Therefore, any exogenous factors that affect inflation in 2016 will affect both output and inflation in 2017. This in turn, will affect both output and inflation in 2018. And so on and on. In this way, output and inflation can change from one period to the next in the DAD-DAS model even if there are no changes in the economys shocks and parameters. The question then is: Does this dynamic process of change eventually come to an end? Long-Run Equilibria The short-run equilibrium at period t is also a long-run equilibrium if, in the absence of shocks, parameter changes, and policy changes, it continues to be the short-run equilibrium in subsequent periods t + 1, t +

2, etc. Short-Run Equilibria that are not Long-Run Equilibria Y 2002 2003 2004 Recall: The height of the DAS at the full-employment output equals the previous periods inflation plus the current periods inflation shock. In this example, there is no inflation shock in 2003 and 2004. DAS2002 DAS2003 DAS2004 B C

D Y04 Y02 Y03 DADall years Lesson: An economy that is in short-run equilibrium but not in long-run equilibrium will changeeven though there are no shocks. The economy will move along DAD towards full employment. Y A Short-Run Equilibrium that is also a Long-Run Equilibrium Y DAS2014

2013 = 2014 A DADall Y2014 years If there are no shocks and all parameters are constant, the outcome at A will continue indefinitely Y Short-Run Equilibria Converge to Long-Run Equilibrium Y 2002 2003 2004 2013 = 2014 DAS2002 DAS2003 DAS2004 B

C D DAS2014 A DADall Y2014 years Y If the economy is at B, it will not stay there. It will move along the DAD curve towards A, the long-run equilibrium. Once the economy reaches A, it will stay there. Short-Run Equilibria Converge to Long-Run Equilibrium 2013 = 2014 Y DAS2014 Z DAS2004 DAS2003

C 2004 2003 DAS2002 B 2002 A DADall Y2014 years Y If there are no shocks and all parameters are constant, an economy initially at A will move along the DAD curve towards Z, the long-run equilibrium. Once at Z, it will stay there. The Long-Run Equilibrium is Stable The last two slides show that: The economy will not stay put if it is at a

short-run equilibrium that is not a long-run equilibrium One such equilibrium leads to another, even if there are no shocks, no parameter changes, and no policy changes The economy invariably ends up in a long-run equilibrium A description of an economy in long-run equilibrium DAD-DAS LONG-RUN EQUILIBRIUM The DAD-DAS models long-run equilibrium This is the normal state around which the economy fluctuates. Definition: The economy is in long-run equilibrium when inflation is stable (), provided there are no shocks () or parameter changes. Long-Run Equilibrium

DAS: In long-run equilibrium all shocks are zero. Therefore, In long-run equilibrium inflation is stable (). Therefore, in long-run equilibrium, GDP is . Long-Run Equilibrium 1 * Yt Yt ( t t ) t DA 1 Y 1 Y D In long-run equilibrium Yt Yt ( t t* ) all shocks are zero 1 Y

We just saw that, in long-run equilibrium, GDP is . Therefore, in long-run equilibrium, inflation is . Moreover, by adaptive expectations, expected inflation is: . Long-Run Equilibrium Y DAS * A DAD Y Long-Run Equilibrium The monetary policy rule is: As and , we see that the long-run nominal interest rate is , and the long-run real interest rate is Solved!

The DAD-DAS models long-run equilibrium To summarize, the long-run equilibrium values in the DAD-DAS theory are essentially the same as the long run theory we saw earlier in this course: Yt Yt rt * t t * t Et t 1 * it t In the short-run, the values of the various variables fluctuate around the long-run equilibrium values. DAD-DAS SHORT-RUN EQUILIBRIUM

Recall: The short-run equilibrium Yt DASt t A In In any any period period t,t, the the intersection intersection of of DAD DADtt and and DAS DAStt determines determines the the short-run short-run equilibrium equilibrium

values values of of inflation inflation and and output at t.t. equilibrium outputIn Inatthe the equilibrium DADt Yt Y shown shown here here at at A, A, output output is is below below its its

natural natural level. level. In In other other words, words, the the DAD-DAS DAD-DAS theory theory is is fully fully capable capable of of explaining explaining recessions recessions and and booms. How does the economy respondin the short run and in the long runto (i) an increase in potential output, (ii) a temporary inflation shock, (iii) a temporary demand shock, and (iv) stricter monetary policy?

DAD-DAS PREDICTIONS 1. Long-Run Growth Suppose an economy is in long-run equilibrium We saw in Chapters 8 and 9 that an economys natural GDP () can increase over time What will be the effect of this on our five endogenous variables in the short-run? In what way will the economy adjust from the old long-run equilibrium to the new long-run equilibrium? Recap: DAD-DAS Slopes and Shifts DAS Upward sloping If natural output increases, shifts right by same amount If previous-period inflation increases, shifts up by same amount If there is a positive inflation shock (),t > 0), shifts up by same amount

DAD Downward sloping If natural output increases, shifts right by same amount If target inflation increases, shifts up by same amount If there is a positive demand shock (t > 0), shifts right 1. Long-run growth t = t + 1 Yt A Yt +1 B

DADt Yt Yt +1 Period Period t:t: initial initial equilibrium equilibrium at at A A Period Period tt + + 11:: LongLongrun run growth growth increases increases the the DASt natural natural rate rate of

of DASt +1 DAS output. shifts output. DAS shifts right right by by the the exact exact amount amount of of the the increase increase in in natural natural GDP. GDP. DAD DAD shifts shifts right right too too by

by the the exact exact amount amount of of the the increase increase in in DADt +1 natural GDP. GDP. Y natural New New equilibrium equilibrium at at B. B. Income Income grows grows but but inflation inflation remains remains 1. Long-run growth

Yt Yt +1 DASt t = t + 1 A B DADt Yt DASt +1 Yt +1 DADt +1 Y

Note that the economy goes directly from one long-run equilibrium, A, to another longrun equilibrium, B, as soon at the natural GDP increases. There is no transition period. 1. Long-Run Growth Therefore, starting from long-run equilibrium, if there is an increase in the natural GDP, actual GDP will immediately increase to the new natural GDP, and none of the other endogenous variables will be affected 2. Inflation Shock Suppose the economy is in long-run equilibrium Then the inflation shock hits for one period (),t > 0) and then goes away (t+1 = 0) How will the economy be affected, both in the short run and in the long run?

Recap: DAD-DAS Slopes and Shifts DAS Upward sloping If natural output increases, shifts right by same amount If previous-period inflation increases, shifts up by same amount If there is a positive inflation shock (t > 0), shifts up by same amount DAD Downward sloping If natural output increases, shifts right by same amount If target inflation increases, shifts up by same amount If there is a positive demand shock (t > 0), shifts right Period Period tt ++ 2:

2: As As inflation inflation falls, falls, A shock to aggregate inflation inflation expectations expectations fall, fall, supply DAS DAS moves moves downward, downward, Y t B C output output rises. rises. Period

Period tt ++ 1: 1: Supply Supply DASt shock = 0) shock is is over over ( (t+1 DASt +1 t+1 = 0) DASt +2 but but DAS DAS does does not not return return to to its its initial initial t t + 2 DASt -1 position

D position due due to to higher higher inflation expectations. inflation expectations. Period shock ( Period t:t: Supply Supply shock (tt >> 0) 0) t 1 A shifts shifts DAS DAS upward; upward; inflation inflation rises, rises, central central bank

bank responds responds by by DAD raising raising real real interest interest rate, rate, output output falls. falls. Y This process Yt Yt + 2 Yt 1 continues until output Period Period tt 1: 1: returns to its natural initial initial equilibrium equilibrium rate. The long run A shock to aggregate supply: one more time Y

2001 + 2002 2002 2003 2004 DAS2002 DAS2003 DAS2004 B C D 2000 = 2001 2002 DAS2001 A DAD Y04 Y02 Y03 Y01

Y 2. Inflation Shock So, we see that if a one-period inflation shock hits the economy, inflation rises at the date the shock hits, but eventually returns to the unchanged long-run level, and GDP falls at the date the shock hits, but eventually returns to the unchanged long-run level What happens to the interest rates i and r? 2. Inflation Shock Y Y Y Y it t t Y Yt Yt it t

rt t * t t * t * t Y Y t t t t According to the monetary policy rule, the temporary spike in inflation dictates an increase in the real interest rate,

whereas the temporary fall in GDP indicates a decrease in the real interest rate The overall effect is ambiguous, for both interest rates We can do simulations for specific values of the parameters and exogenous variables Recall: The Solution! As we saw before, it is possible to express output and inflation entirely in terms of exogenous variables, parameters, shocks and pre-determined inflation. The monetary policy rule can then be used to solve for the nominal interest rate. The Fisher equation can be used to solve for the real interest rate. These solutions can be used to simulate the future outcomes for given values of the exogenous Parameter values for simulations Thus, we can interpret as the percentage Yt 100 * t 2.0 1.0 2.0 0.25

0.5 Y 0.5 Thus, we can interpret as the percentage deviation deviation of of output output from from its its natural natural level. level. The The central central banks banks inflation inflation target target is is 22 percent. percent. AA 1-percentage-point 1-percentage-point increase increase in in the the real real interest

interest rate rate reduces reduces output output demand demand by by 11 percent percent of of its its natural natural level. level. The The natural natural rate rate of of interest interest is is 22 percent. percent. When When output output is is 11 percent percent above above its its natural

natural level, level, inflation inflation rises rises by by 0.25 0.25 percentage percentage point. point. These These values values are are from from the the Taylor Taylor Rule, Rule, which which approximates approximates the the actual actual behavior behavior of of the the Federal Federal Reserve.

Reserve. Impulse Response Functions The following graphs are called impulse response functions. They show the response of the endogenous variables to the impulse, i.e. the shock. The graphs are calculated using our assumed values for the exogenous variables and parameters The dynamic response to a supply shock t Yt AA one-period one-period supply supply shock shock affects affects output output for

for many many periods. periods. The dynamic response to a supply shock t t Because Because inflation inflation expectations expectations adjust adjust slowly, slowly, actual actual inflation inflation remains remains high high for

for many many periods. periods. The dynamic response to a supply shock t rt The The real real interest interest rate rate takes takes many many periods periods to to return return to to its its

natural natural rate. rate. The dynamic response to a supply shock The The behavior behavior t it of of the the nominal nominal interest interest rate rate depends depends on on that that of

of inflation inflation and and real real interest interest rates. rates. 3. A Series of Aggregate Demand Shocks Suppose the economy is at the long-run equilibrium Then a positive aggregated demand shock hits the economy for five successive periods (t= t+1= t+2= t+3= t+4 > 0), and then goes away (t+5 = 0) How will the economy be affected in the short run? That is, how will the economy adjust over time? Recap: DAD-DAS Slopes and Shifts DAS Upward sloping If natural output

increases, shifts right by same amount If previous-period inflation increases, shifts up by same amount If there is a positive inflation shock (),t > 0), shifts up by same amount DAD Downward sloping If natural output increases, shifts right by same amount If target inflation increases, shifts up by same amount If there is a positive demand shock (t > 0), shifts right Period Period tt 1: 1: initial initial equilibrium

equilibrium at A at A Period t: Positive Period t: Positive demand demand DASt +5 shock 0) shifts shock t( (++>>1: 0)Higher shifts AD AD to to Period Period t 1: Higher Y the

output and the right; right; output and DASt +4 inflation in t raised inflation in t raised inflation Periods t + 2 to t ++inflation 4: Periods t +

2 to t 4: inflation rise. inflation rise. expectations for t + 1, expectations forin + 1, DASt +3 Higher Higher inflation inflation int previous previous F shifting DAS Inflation shifting

DAS up. up. Inflation period raises inflation period raises inflation DASt +2 rises more, rises more, output output falls. expectations, shifts DAS E expectations, shiftsfalls. DAS Period t + 5: DAS

is Period t + 5:rises, DAS output is Inflation up. Inflation rises, output DASt + 1 up. D higher higher due due to to higher higher falls. falls. C inflation in in preceding preceding DASt -1,t inflation period, period, but but demand

demand shock shock B ends and ends and DAD DAD to Periods tt ++ returns 6returns Periods 6 and and to its position. its initial initial position. higher: higher: DADt ,t+1,,t+4Equilibrium at A Equilibrium at G.

G. shifts DAS DAS gradually gradually shifts down down as as inflation inflation and and DADt -1, t+5 inflation inflation expectations expectations Y fall. Yt 1 Yt fall. The The economy economy gradually gradually recovers recovers and and reaches reaches the

the long long run run equilibrium equilibrium at at A. A. A shock to aggregate demand t + 5 G t t 1 Yt + 5 A 3-period shock to aggregate demand Y DAS04 DAS03 0

D 3 0 DAS02 C 0 2 B DAS00,01 1 1999 = 00 DAD01,02,03 A DAD00,04 Y00 Y03 Y02Y01

Y When the demand shock first hits, output and inflation both increase. In the two following periods, despite the continuing presence of the demand shock, output starts to fall. Inflation continues to rise. 3. A shock to aggregate demand Y 0 3 0 0 DAS04 DAS05 DAS06 E F DAS00,01 4 5 1999 = 00

A DAD00,04,05,06 Y04 Y05 Y00 Y On the date the demand shock ends, output falls below the long-run level and inflation finally begins to fall. After that, output rises and inflation falls towards the initial long-run equilibrium. 3. A 3-period shock to aggregate demand Y Counterclockwise cycle 0 3 0 0 0 D

E F C 4 2 50 Clockwise cycle B unemployment 1 1999 = 00 A Y04 Y05 Y00 Y03 Y02Y01

Y In short, after a positive demand shock we get a counter-clockwise cycle in the output-inflation graph. But this is also a clockwise cycle in the unemployment-inflation graph. Inflation-Unemployment Cycles Please see: http://krugman.blogs.nytimes.com/2010/07/31 /clockwise-spirals / http://krugman.blogs.nytimes.com/2011/11/17/ subsiding-inflation / http:// krugman.blogs.nytimes.com/2012/04/08/une A Series of Aggregate Demand Shocks: 4 Phases 1. On the date the multi-period demand shock first hits, both output and inflation rise above their long-run values 2. After that, while the demand shock is still present, output falls and inflation continues to rise 3. On the date the demand shock ends, output falls

below its long-run value and inflation falls 4. After that, output recovers and inflation falls, gradually returning to their original long-run values What happens to the interest rates i and r? A Series of Aggregate Demand Shocks: 4 Phases, interest rates 1. On the date the multi-period demand shock first hits, both output and inflation rise above their long-run values. So, interest rate rises 2. After that, while the demand shock is still present, output falls and inflation continues to rise. Now, the effect on the interest rate is ambiguous 3. On the date the demand shock ends, output falls below its long-run value and inflation falls. So, the interest rate falls 4. After that, output recovers and inflation falls, gradually returning to their original long-run values. Again, the effect on the interest rate is ambiguous, but it does return to its original long run value ()) The dynamic response to a demand shock t Yt The

The demand demand shock shock raises raises output output for for five five periods. periods. When When the the shock shock ends, ends, output output falls falls below below its its natural natural level, level, and

and recovers recovers gradually. gradually. The dynamic response to a demand shock t t The The demand demand shock shock causes causes inflation inflation to to rise. rise. When When the the shock

shock ends, ends, inflation inflation gradually gradually falls falls toward toward its its initial initial level. level. The dynamic response to a demand shock t rt The The demand demand shock shock raises raises the

the real real interest interest rate. rate. After After the the shock shock ends, ends, the the real real interest interest rate rate falls falls and and approaches approaches its its initial initial level. level.

The dynamic response to a demand shock The The behavior behavior t it of of the the nominal nominal interest interest rate rate depends depends on on that that of of the the inflation

inflation and and real real interest interest rates. rates. 4. Stricter Monetary Policy Suppose an economy is initially at its longrun equilibrium Then its central bank becomes less tolerant of inflation and reduces its target inflation rate ()*) from 2% to 1% What will be the short-run effect? How will the economy adjust to its new long-run equilibrium? Recap: DAD-DAS Slopes and Shifts DAS Upward sloping If natural output increases, shifts right by same amount If previous-period inflation increases, shifts up by same

amount If there is a positive inflation shock (),t > 0), shifts up by same amount DAD Downward sloping If natural output increases, shifts right by same amount If target inflation increases, shifts up by same amount If there is a positive demand shock (t > 0), shifts right Period Period tt 1: 1: target target inflation inflation rate rate * * == 2%, 2%, initial

initial equilibrium equilibrium at at A A A shift in monetary policy Y t 1 = 2% t DASt -1, t DASt +1 A B C DASfina l final = 1% Z DADt 1

DADt, t + 1, Yt Yt 1 , Yfinal Y Period Period t:t: Central Central bank bank lowers lowers target target to to * * == 1%, 1%, raises raises real real interest interest rate, rate, shifts shifts

DAD DAD leftward. leftward. Output Output and and inflation inflation fall. fall. Period Period tt ++ 1: 1: The The fall fall in in ttreduced reduced inflation inflation expectations expectations for for tt ++ 1, 1, shifting shifting DAS DAS downward. downward. Output

Output rises, rises, inflation inflation falls. falls. Subsequent Subsequent periods: periods: This This process process continues continues until until output output returns returns to to its its natural natural rate rate and and inflation inflation reaches reaches its its

4. Stricter Monetary Policy At the date the target inflation is reduced, output falls below its natural level, and inflation falls too towards its new target level The real interest rate rises above its natural level ()) The effect on the nominal interest rate (i = r + ) is ambiguous On the following dates, output recovers and gradually returns to its natural level. Inflation continues to fall and gradually approaches the new target level. The real interest rate falls, gradually returning to its natural level ()) The nominal interest rate falls to its new and lower long-run level (i = ) + *) The dynamic response to a reduction in target inflation t* Yt Reducing Reducing the the target

target inflation inflation rate rate causes causes output output to to fall fall below below its its natural natural level level for for aa while. while. Output Output recovers recovers gradually. gradually. The dynamic response to a reduction in

target inflation t* t Because Because expectations expectations adjust adjust slowly, slowly, itit takes takes many many periods periods for for inflation inflation to to reach reach the the

new new target. target. The dynamic response to a reduction in target inflation t* rt To To reduce reduce inflation, inflation, the the central central bank bank raises raises the the real real interest interest rate

rate to to reduce reduce aggregate aggregate demand. demand. The The real real interest interest rate rate gradually gradually returns returns to to its its natural natural rate. rate. The dynamic response to a reduction in target inflation

t* it The The initial initial increase increase in in the the real real interest interest rate rate raises raises the the nominal nominal interest interest rate. rate. As As the

the inflation inflation and and real real interest interest rates rates fall, fall, the the nominal nominal rate rate falls. falls. APPLICATION: Output variability vs. inflation variability A supply shock reduces output (bad) and raises inflation (also bad). The central bank faces a tradeoff between these bads it can reduce the effect on output,

but only by tolerating an increase in the effect on inflation. The DAD Equation 1 * Yt Yt ( t t ) t 1 Y 1 Y CASE 1: is large, Y is small Therefore, a small increase in inflation is accompanied by a large decrease in output That is, the DAD curve is flat See the next slide APPLICATION: Output variability vs. inflation variability CASE 1: is large, Y is small A

A supply supply shock shock shifts shifts DAS DAS up. up. DASt DASt 1 t t 1 DADt 1, t Yt Yt 1 Y In In this this case, case, aa small small change

change in in inflation inflation has has aa large large effect effect on on output, output, so so DAD DAD is is relatively relatively flat. flat. The The shock shock has has aa large large effect effect on on output, output, but but aa small

small effect effect on on inflation. inflation. The DAD Equation 1 * Yt Yt ( t t ) t 1 Y 1 Y CASE 2: is small, Y is large Therefore, even a large increase in inflation is accompanied by only a small decrease in output That is, the DAD curve is steep See the next slide APPLICATION: Output variability vs. inflation variability CASE 2: is small, Y is large

DASt t DASt 1 t 1 DADt 1, t Yt Yt 1 Y In In this this case, case, aa large large change change in in inflation inflation has has only only aa small small effect

effect on on output, output, so so DAD DAD is is relatively relatively steep. steep. Now, Now, the the shock shock has has only only aa small small effect effect on on output, output, but but aa big big effect effect on on inflation.

inflation. APPLICATION: Output variability vs. inflation variability The central bank must decide whether it wants Less variability in inflation, or Less variability in output It cant have less variability in both inflation and output APPLICATION: The Taylor Principle The Taylor Principle (named after economist John Taylor): The proposition that a central bank should respond to an increase in inflation with an even greater increase in the nominal interest rate (so that the real interest rate rises). I.e., central bank should set > 0. Otherwise, DAD will slope upward, economy may be unstable, and inflation may spiral out of control. APPLICATION:

The Taylor Principle 1 * Yt Yt ( t t ) t 1 Y 1 Y it t ( t t* ) Y (Yt Yt ) (DAD) (MP rule) If > 0: When inflation rises, the central bank increases the nominal interest rate even more, which increases the real interest rate and reduces the demand for goods and services. DAD has a negative slope. APPLICATION: The Taylor Principle

1 * Yt Yt ( t t ) t 1 Y 1 Y it t ( t t* ) Y (Yt Yt ) (DAD) (MP rule) If < 0: When inflation rises, the central bank increases the nominal interest rate by a smaller amount. The real interest rate falls, which increases the demand for goods and services. DAD has a positive slope. APPLICATION: The Taylor Principle If DAD is upward-sloping and steeper than DAS, then the economy is unstable: output will not return to its natural level, and inflation will spiral upward (for positive demand shocks) or downward (for

negative ones). Estimates of from published research: = 0.14 from 1960-78, before Paul Volcker became Fed chairman. Inflation was high during this time, especially during the 1970s. = 0.72 during the Volcker and Greenspan years. Inflation was much lower during these years. See A Simple Treatment of the Liquidity Trap for Intermediate Macroeconomics Courses, The Journal of Economic Education, 45(1), 36-55, 2014. PDF copy available at http://myweb.liu.edu/~ uroy/resume/myPDF/JEE-2014.pdf. DAD-DAS + ZLB! DAD-DAS + ZLB! When the nominal interest rate is a positive number, we have seen that the DAD equation is When the central bank wants to set the nominal interest rate at a negative number, it wont get its wish. It will be forced to set . In this case, the DAD equation becomes Why?

The Dynamic Aggregate Demand Curve (ZLB) The Demand Equation t Y Yt (rt ) t rt it Et t 1 Yt Yt ( it Et t 1 ) t Yt Yt ( it t ) t ( )+ = + ( + ) + = Surprise, the DAD curve is now positively sloped! Fisher

Fisher equation equation Et t 1 t adaptive adaptive expectation expectation ss = Zero Lower Bound t * O The regular DAD is negatively-sloped: Yt The DAD at ZLB is positively-sloped:

D There are two long-run equilibria: O and D! The long-run equilibrium that the textbook discusses is O, the orthodox long-run equilibrium. The new one is D, the deflationary long-run equilibrium, for the ZLB world. t * O R r R R DASO (t 1 = *; t =

0) D D If inflation is higher than , the negative of the natural real interest rate, at any date, there is nothing to DASR (t 1 = R < r; t = 0)worry: the economy will converge R gradually to the long-run equilibrium at O. Yt DASD (t 1 = ); t = 0) There are two long-run equilibria: O and D! The long-run equilibrium that the textbook discusses is O, the orthodox long-run equilibrium. The new one is D, the deflationary long-run equilibrium, for the ZLB world.

The new long-run equilibrium at D is unstable! For example, if the economy is at B, it will move to F and then to G, etc. In other words, the economy will move away from the long-run equilibrium at D and enter a deflationary spiral. Output and inflation will both keep falling and falling. Very scary! The natural real interest rate () has been falling since the 1980s and has become negative lately.

The natural real interest rate () has been falling since the 1980s and has become negative lately. This brings the deflationary longrun equilibrium, D, closer to the stable long-run equilibrium, O. This increases the chance that a shock could throw a perfectly fine economy into the dreaded deflationary spiral. Very scary! DAD-DAS + ZLB!

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