N. Gregory Mankiw PowerPoint Slides by Ron Cronovich CHAPTER 14 A Dynamic Model of Aggregate Demand and Aggregate Supply 2010 Worth Publishers, all rights reserved SEVENTH EDITION MACROECONOMICS In this chapter, you will learn: how to incorporate dynamics into the AD-AS model we previously studied how to use the dynamic AD-AS model to illustrate long-run economic growth how to use the dynamic AD-AS model to trace out the effects over time of various shocks and policy changes on output, inflation, and other endogenous variables The difficulty with the basic model arises from the following two assumptions we made: 1.That the economy does not experience continuing inflation and 2.That the economy does not experience long-run growth Dynamic model of AD and AS makes three changes to the basic model: 1.Potential real GDP increases continually, shifting the longrun aggregate supply curve to the right 2.During most years, the aggregate demand curve will be shifting to the right. 3. Except during period when workers and firms expect high rates of inflation, the short-run aggregate supply curve will be shifting to the right.
3 Introduction Themodels These dynamic are model of aggregate demand and dynamic because they gives trace the of insight variablesinto overhow aggregate supply uspath more time. the economy works in the short run. stochastic because they incorporate the inherent randomness of economic life. of a DSGE model, It is a simplified version general equilibrium because they take into account the used in cutting-edge macroeconomic research. fact that everything depends on everything else. (DSGE = Dynamic, Stochastic, General In many ways, they are the state-of-the-art models in the Equilibrium) analysis of short run economic fluctuations. 4 Introduction The dynamic model of aggregate demand and aggregate supply is built from familiar concepts,
such as: the IS curve, which negatively relates the real interest rate and demand for goods & services the Phillips curve, which relates inflation to the gap between output and its natural level, expected inflation, and supply shocks adaptive expectations, a simple model of inflation expectations 5 How the dynamic AD-AS model is different from the standard model In explicitly incorporates the response of monetary policy to economic conditions. Instead of fixing the money supply, the central bank follows a monetary policy rule that adjusts interest rates when output or inflation change. The vertical axis of the DAD-DAS diagram measures the inflation rate, not the price level. Subsequent time periods are linked together: Changes in inflation in one period alter expectations of future inflation, which changes aggregate supply in future periods, which further alters inflation and inflation expectations. 6 Keeping track of time The subscript t denotes the 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 7
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 equations may use different notation, but they are conceptually similar to things youve already learned. The first equation is for output 8 Output: The Demand for Goods and Services Yt Yt (rt ) t output natural level of output real interest rate 0, 0 Negative Negative relation relation between between output output and and interest interest rate, rate, same
same intuition intuition as as IS IS curve. curve. 9 Output: The Demand for Goods and Services Yt Yt (rt ) t measures the interest-rate sensitivity of demand natural rate of interest in absence of demand shocks, Yt Yt when rt demand shock, random and zero on average 10 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, Et t 1 not known in period t expectation, formed in period t, of inflation from t to t +1 11 Inflation: The Phillips Curve t Et 1 t (Yt Yt ) t current inflation previously expected inflation 0 indicates how much supply shock, random and zero on average inflation responds when output fluctuates around its natural level 12 Expected Inflation: Adaptive Expectations
Et t 1 t For For simplicity, simplicity, we we assume assume people people expect expect prices prices to to continue continue rising rising at at the the current current inflation inflation rate. rate. 13 The Nominal Interest Rate: The Monetary-Policy Rule * t it t ( t ) Y (Yt Yt ) nominal interest rate, set each period by the central bank central banks inflation target natural rate of
interest 0, Y 0 the central banks policy parameters 14 The Nominal Interest Rate: The Monetary-Policy Rule * t it t ( t ) Y (Yt Yt ) measures how much the central bank adjusts the interest rate when inflation deviates from its target measures how much the central bank adjusts the interest rate when output deviates from its natural rate Theta_pi will be high relative to theta_Y if the central bank considers fighting inflation more important than fighting unemployment. 15 CASE STUDY 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. 16 CASE STUDY The Taylor Rule actual Federal Funds rate Taylors rule The models variables and parameters Endogenous variables: Yt Output t Inflation rt Real interest rate it Nominal interest rate Et t 1 Expected inflation 18 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 19 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 20 The models long-run equilibrium The normal state around which the economy fluctuates. Two conditions required for long-run equilibrium: There are no shocks: t t 0 Inflation is constant: t 1 t 21
The models long-run equilibrium Plugging the preceding conditions into the models five equations and using algebra yields these long-run values: Yt Yt rt * t t * t Et t 1 * it t 22 The Dynamic Aggregate Supply Curve The DAS curve shows a relation between output and inflation that comes from the Phillips Curve and Adaptive Expectations: t t 1 (Yt Yt ) t (DAS) The parameters of the monetary policy rule influence the slope of the DAS curve, so they determine whether a supply shock has a greater effect on output or inflation. Thus, the central bank faces a tradeoff between output variability and inflation variability. 23 The Dynamic Aggregate Supply Curve t t 1 (Yt Yt ) t DASt
DAS DAS slopes slopes upward: upward: high high levels levels of of output output are are associated associated with with high high inflation. inflation. DAS DAS shifts shifts in in response response to to changes changes in in the the natural natural level level of of output, output, previous previous inflation, inflation, and supply supply shocks. shocks. Y and
24 The Dynamic Aggregate Demand Curve To derive the DAD curve, we will combine four equations and then eliminate all the endogenous variables other than output and inflation. Start with the demand for goods and services: Yt Yt (rt ) t using using the the Fisher Fisher eqn eqn Yt Yt ( it Et t 1 ) t 25 The Dynamic Aggregate Demand Curve result result from from previous previous slide slide Yt Yt ( it Et t 1 ) t Yt Yt ( it t ) t using using the the expectations expectations eqn eqn using using monetary monetary policy
policy rule rule Yt Yt [ t ( t t* ) Y (Yt Yt ) t ] t Yt Yt [ ( t t* ) Y (Yt Yt )] t 26 The Dynamic Aggregate Demand Curve result result from from previous previous slide slide Yt Yt [ ( t t* ) Y (Yt Yt )] t combine combine like like terms, terms, solve solve for for Y Y * t Yt Yt A( t ) B t , (DAD) 1 0, B 0 where A 1 Y 1 Y 27
The Dynamic Aggregate Demand Curve * t Yt Yt A( t ) B t 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 & & services. services. DADt Y DAD
DAD shifts shifts in in response response to to changes changes in in the the natural natural level level of of output, output, the the inflation inflation target, target, and and demand demand shocks. shocks. 28 The short-run equilibrium Yt DASt t A In In each each period, period, the the intersection
intersection of of DAD DAD and and DAS DAS determines determines the the short-run short-run eqm eqm values values of of inflation inflation and and output. output. DADt Yt Y In In the the eqm eqm shown shown here here at at A, A, output output is is below below its its natural
natural level. level. 29 Long-run growth t = t t + 1 Yt A Yt +1 B DADt Yt Yt +1 DAS Period tt:: shifts DAS shifts Period because initial eqm because initial eqm at at A A
economy economy can can produce DASt produce more more DASt +1 g&s g&s Period Period tt ++ 11 :: Long-run New Long-run eqm at New eqm at B, B, DAD shifts DAD shifts growth income growth grows income grows because because increases the but increases inflation the but
inflation higher income higher income natural rate remains natural stable. rate remains stable. raises raises of of output. output. demand demand DADt +1 for for g&s g&s Y 30 A shock to aggregate supply Y t t + 2 t 1 DASt DASt +1 DASt +2 B
C D DASt -1 A DAD Yt Yt + 2 Yt 1 Y Period :+:12211:::: Period Periodtttt+ Period initial eqm at Supply shock Supply shock initial eqm at A A Supply shock Supply shock As inflation falls, As inflation falls, ((over >> 0) is
shifts inflation 0)((shifts is over == 0) 0) inflation DAS upward; but DAS does not expectations DAS upward; but DAS doesfall, not expectations fall, inflation rises, return to initial DAS moves inflation rises, return to its its initial DAS moves central position
due downward, central bank bank position due to to downward, responds by higher inflation output rises. responds by higher inflation output rises. raising real expectations. raising real expectations. This process interest interest rate, rate, continues until output falls. outputreturns falls. to output its natural rate. LR eqm at A.
31 Parameter values for simulations Yt 100 t* 2.0 1.0 2.0 0.25 0.5 Y 0.5 Thus, Thus, we we can can interpret interpret Yt Yt as the percentage deviation of as the percentage deviation of Central banks inflation Centralfrom banks inflationlevel. output its natural outputisfrom its natural level.
target 2 percent. A 1-percentage-point increase target is 2 percent. A 1-percentage-point increase The following called The following graphs graphs are are called in interest reduces in the the real real interest rate rate reduces impulse response functions. impulse response functions. output demand by 11 percent of
output demand by percent of They show the response of They show the response of The natural rate of interest is The natural rate of interest is its natural level. its natural level. variables to the endogenous 2the percent. endogenous variables to 2 percent. When output is
1 percent When output is 1 the percent the impulse, i.e. shock. the impulse, i.e. the shock. above its natural level, above its natural 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. 32 The dynamic response to a supply shock t Yt AA oneoneperiod 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
expectexpectations ations 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 t it The The behavior behavior 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. A shock to aggregate demand Y t + 5 DASt +5 DASt +4 DASt +3 DASt +2 F G E DASt + 1 D C t B t 1 DADt ,t+1,,t+4 A DADt -1, t+5 Yt + 5
Yt 1 DASt -1,t Yt Y :t+ Period :tt++ Period Periods t+ Period t+ Periods Period Periods Period ttttt+ 1+ Periods Period 15+5116::6::2:2 Positive initial Positive and higher: DAS is higher initial at A Ain and higher: DAS is4eqm
higher Higher inflation to tt + :: at Higher inflation in to + 4eqm demand shock demand shock DAS gradually to higher DAS gradually due to higher ttdue Higher raised inflation inflation Higher raised inflation (( previous >> 0) shifts shifts down inflation in
0) shifts shifts down as inflation in as in expectations in previous expectations AD to right; inflation and preceding period, AD to11the the right; inflation and preceding period, period for tt ++ ,raises period for ,raises output and inflation but demand output and up.
inflation but demand inflation shifting DAS inflation shifting DAS up. inflation rise. expectations fall, shock ends and inflation rise. expectations shock ends and expectations, Inflation rises expectations, Inflation rises fall, DAD returns to DAD returns to shifts DAS up. more, output falls.
shifts DAS up. more, output falls. economy its initial economy its initial position. position. Inflation rises, Inflation rises, gradually gradually output output falls. falls. recovers until Eqm at recovers until Eqm at G. G. reaching reaching LR LR eqm eqm at at A. A. 37 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 t it The The behavior behavior 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. 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 tt tt::11:: Period Period Period
Period t + 1 :: Period t + 1 target inflation Central bank target inflation Central bank Subsequent Subsequent The fall in tt The fall intarget lowers rate * = 2%, lowers target rate * = 2%, periods: periods:
reduced reduced initial eqm at A initial eqm at A This process This process inflation inflation to to ** == 1%, 1%, continues until continues until expectations expectations raises real raisesreturns real output output returns for tt ++ 1, forinterest 1, rate, interest rate, to its
natural to its natural shifting DAS shifting DAS shifts DAD shifts DAD rate and rate and downward. downward. leftward. leftward. inflation inflation Output rises, Output rises, Output and Output and reaches its reaches its new new inflation falls. inflation falls. inflation
inflation fall. fall. target. target. 42 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 expectexpectations ations 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 parameters of the monetary policy rule influence the slope of the DAS curve, so they determine whether a supply shock has a greater effect on output or inflation. Thus, the central bank faces a tradeoff between output variability and inflation variability. 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 * t Y Yt Yt [ ( t ) Y (Yt Yt )] t 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. 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: The Taylor Principle The Taylor Principle (named after 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. 50 APPLICATION: The Taylor Principle If > 0: When inflation rises, the central bank increases the nominal interest rate even more, which increases the real interest rate rt it Et t 1 and reduces the demand for goods & services. it t ( t t* ) Y (Yt Yt ) (MP rule) DAD has a negative slope.
1 * Yt Yt ( t t ) t 1 Y 1 Y (DAD) 51 APPLICATION: The Taylor Principle If < 0: When inflation rises, the central bank increases the nominal interest rate by a smaller amount. The real interest rate falls rt it Et t 1 , which increases the demand for goods & services. * t it t ( t ) Y (Yt Yt ) (MP rule) DAD has a positive slope. 1 * Yt Yt ( t t ) t 1 Y 1 Y (DAD) 52
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. 53 Readings and Assignments Kydland, Finn and Prescott, Edward (1977), Rules Rather than Discretion: The Inconsistency of Optimal Plans, Journal of Political Economy, Vol. 85, No. 3, pp. 473-491. Barro, Robert and Gordon, David (1983), Rules, Discretion, and Reputation in a Model of Monetary Policy, Journal of Monetary Economics, Vol. 12, pp. 101-121. Mankiws textbook Review questions 1-4 Problems questions 2, 6 and 8 54 Chapter Summary The DAD-DAS model combines five relationships: an IS-curve-like equation of the goods market, the Fisher equation, a Phillips curve equation, an
equation for expected inflation, and a monetary policy rule. The long-run equilibrium of the model is classical. Output and the real interest rate are at their natural levels, independent of monetary policy. The central banks inflation target determines inflation, expected inflation, and the nominal interest rate. Chapter Summary The DAD-DAS model can be used to determine the immediate impact of any shock on the economy, and can be used to trace out the effects of the shock over time. The parameters of the monetary policy rule influence the slope of the DAS curve, so they determine whether a supply shock has a greater effect on output or inflation. Thus, the central bank faces a tradeoff between output variability and inflation variability. Chapter Summary The DAD-DAS model assumes that the Taylor Principle holds, i.e. that the central bank responds to an increase in inflation by raising the real interest rate. Otherwise, the economy may become unstable and inflation may spiral out of control.
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