#### Transcript A Dynamic Model of Aggregate Demand and Aggregate Supply

A Dynamic Model of Aggregate Demand and Aggregate Supply Chapter 14 of Macroeconomics, 7th 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 • In this chapter, that silence will end • This chapter presents a dynamic model of aggregate demand and aggregate supply (DAD-DAS) Introduction • The dynamic model of aggregate demand and aggregate supply (DAD-DAS) gives us more insight into how the economy behaves in the short run. • This theory determines both real GDP (Y) and the inflation rate (π) • 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 that adjusts interest rates automatically when output or inflation are not where they should be. Introduction 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 model’s 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… Output: The Demand for Goods and Services Yt Yt (rt ) t output natural level of output real interest rate 0, 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. 10. Output: The Demand for Goods and Services Yt Yt (rt ) t measures the interest-rate sensitivity of demand “natural rate of interest” This is the long-run real interest rate we had calculated in Ch. 3 Note that in the absence of demand shocks, Yt Yt when rt demand shock, random and zero on average The demand shock is positive when C0, I0, or G is higher than usual or T is lower than usual. IS Curve = Demand Equation r rt IS Y Yt r rt The long-run real interest rate of Ch. 3 is now denoted by the lower-case Greek letter ρ. IS Yt Y IS Curve = Demand Equation r rt IS Y Yt r rt IS Yt Y 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 t 1 rt it Et t 1 nominal interest rate expected inflation rate 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. 4 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 Expected Inflation: Adaptive Expectations Et t 1 t Assumption: people expect prices to continue rising at the current inflation rate. Examples: E2000π2001 = π2000; E2010π2011 = π2010; etc. 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 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 bank’s 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 – GDP gap = 100 x Y Y Y = percent by which real GDP is below its natural rate • The Taylor Rule matches Fed policy fairly well.… CASE STUDY 10 9 8 Percent 7 The Taylor Rule actual Federal Funds rate 6 5 4 3 2 1 Taylor’s rule 0 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 SUMMARY OF THE DAD-DAS MODEL The model’s variables and parameters • Endogenous variables: Yt Output t Inflation rt Real interest rate it Nominal interest rate Et t 1 Expected inflation The model’s variables and parameters • Exogenous variables: Yt Natural level of output Central bank’s target inflation rate t Demand shock t Supply shock * t • Predetermined variable: t 1 Previous period’s inflation The model’s 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 Y Responsiveness of i to inflation in the monetary-policy rule 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 Phillips Curve Et t 1 t Adaptive Expectations it t t Y Yt Yt * t Monetary Policy Rule THE LONG RUN EQUILIBRIUM The DAD-DAS model’s long-run equilibrium • This is the normal state around which the economy fluctuates. • The economy is in long-run equilibrium when: t t 0 – There are no shocks: – Inflation is stable: t 1 t The DAD-DAS model’s long-run equilibrium Et t 1 t Adaptive Expectations Et 1 t t 1 t Et 1 t Yt Yt t Phillips Curve t t 1 Yt Yt t Recall that the long-run equilibrium requirements are: t t 0 DAS Curve t 1 t The DAD-DAS model’s long-run equilibrium Yt Yt (rt ) t Recall that the long-run equilibrium requirements include: Demand Equation t t 0 The DAD-DAS model’s long-run equilibrium Fisher Equation Adaptive Expectations rt it Et t 1 Et t 1 t Therefore, in the DAD-DAS theory, the (ex ante) real interest rate is the current nominal interest rate minus the inflation rate just observed. rt it t The DAD-DAS model’s long-run equilibrium rt it Et t 1 Et t 1 t rt it t it t t it Monetary Policy Rule it t t Y Yt Yt * t The DAD-DAS model’s 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 Et t 1 * it t * t SHORT-RUN FLUCTUATIONS AROUND THE LONG RUN Recap: Dynamic Aggregate Supply t Et 1 t Yt Yt t Phillips Curve Adaptive Expectations Et t 1 t Et 1 t t 1 t t 1 Yt Yt t DAS Curve The Dynamic Aggregate Supply Curve t t 1 (Yt Yt ) t π DAS slopes upward: high levels of output are associated with high inflation. DASt t 1 t Y Yt The Dynamic Aggregate Supply Curve t t 1 (Yt Yt ) t π DAS2011 2010 2011 If you know (a) the natural GDP at a particular date, (b) the inflation shock at that date, and (c) the previous period’s inflation, you can figure out the location of the DAS curve at that date. Y Y2011 The Dynamic Aggregate Supply Curve t t 1 (Yt Yt ) t π DAS2015 2014 2015 If you know (a) the natural GDP at a particular date, (b) the inflation shock at that date, and (c) the previous period’s inflation, you can figure out the location of the DAS curve at that date. Y Y2015 Shifts of the DAS Curve t t 1 (Yt Yt ) t π Any increase (decrease) in the previous period’s inflation or in the current period’s inflation shock shifts the DAS curve up (down) by the same amount DASt t 1 t Y Yt Shifts of the DAS Curve t t 1 (Yt Yt ) t π Any increase (decrease) in the previous period’s inflation or in the current period’s inflation shock shifts the DAS curve up (down) by the same amount DASt t 1 t Any increase (decrease) in natural GDP shifts the DAS curve right (left) by the exact amount of the change. Y Yt The Dynamic Aggregate Demand Curve The Demand Equation Yt Yt (rt ) t rt it Et t 1 Fisher equation Yt Yt ( it Et t 1 ) t Yt Yt ( it t ) t Et t 1 t adaptive expectations The Dynamic Aggregate Demand Curve it t t Y Yt Yt * t monetary policy rule Yt Yt ( it t ) t Yt Yt [ t ( t t* ) Y (Yt Yt ) t ] t Yt Yt [ ( t ) Y (Yt Yt )] t * t We’re almost there! Dynamic Aggregate Demand Yt Yt [ ( t ) Y (Yt Yt )] t * t Yt Yt ( t ) Y Yt Y Yt t * t Yt Y Yt Yt ( t ) Y Yt t * t (1 Y ) Yt (1 Y ) Yt ( t ) t * t 1 * Yt Yt ( t t ) t 1 Y 1 Y Yt Yt A ( t ) B t * t This is the equation of the DAD curve! The Dynamic Aggregate Demand Curve π Yt Yt A( t t* ) Bt DAD slopes downward: When inflation rises, the central bank raises the real interest rate, reducing the demand for goods and services. DADt Y Note that the DAD equation has no dynamics in it, because it only shows how simultaneously measured variables are related to each other The Dynamic Aggregate Demand Curve π Yt Yt A( t t* ) Bt t* DADtB Yt B t Y The Dynamic Aggregate Demand Curve π Yt Yt A( t t* ) Bt When the central bank’s target inflation rate increases (decreases) the DAD curve moves up (down) by the exact same amount. t* DADtA DADtB Yt B t Y The Dynamic Aggregate Demand Curve π Yt Yt A( t t* ) Bt When the natural rate of output increases (decreases) the DAD curve moves right (left) by the exact same amount. t* DADtA When there is a positive (negative) demand shock the DAD curve moves right (left) . DADtB Yt B t Y A positive demand shock could be an increase in C0, I0, or G, or a decrease in T. The Dynamic Aggregate Demand Curve π 1 * Yt Yt ( t t ) t 1 Y 1 Y DADtA DADtB The DAD curve shifts right or up if: (a) the central bank’s target inflation rate goes up, (b) there is a positive demand shock, or (c) the natural rate of output increases. Y Summary: 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 (νt > 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 (εt > 0), shifts right DAD-DAS EQUILIBRIUM The short-run equilibrium π Yt DASt πt A In each period, the intersection of DAD and DAS determines the shortrun equilibrium values of inflation and output. DADt Yt Y In the equilibrium shown here at A, output is below its natural level. In other words, the DAD-DAS theory is fully capable of explaining recessions and booms. DAD-DAS PREDICTIONS Long-Run Growth 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 (νt > 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 (εt > 0), shifts right Long-run growth Yt π πt = πt + 1 A DASt +1 B DADt Yt Period t + 1: Long-run growth increases the natural rate of output. Yt +1 DASt Yt +1 Period t: initial equilibrium at A DADt +1 Y DAS shift right by the exact amount of the increase in natural GDP. DAD shifts right too by the exact amount of the increase in natural GDP. New equilibrium at B. Income grows but inflation remains stable. 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 Inflation Shock • Suppose the economy is in long-run equilibrium • Then the inflation shock hits for one period (νt > 0) and then goes away (νt+1 = 0) • How will the economy be affected, both in the short run and in the long run? A shock to Period t + 2: As inflation falls, inflation expectations fall, DAS aggregate supply moves downward, output rises. Y π πt πt + 2 B C D DASt DASt +1 DASt +2 DASt -1 Period t + 1: Supply shock is over (νt+1 = 0) but DAS does not return to its initial position due to higher inflation expectations. Period t: Supply shock (νt > 0) shifts πt – 1 DAS upward; inflation rises, central A bank responds by raising real DAD interest rate, output falls. Y This process continues Yt Yt + 2 Yt –1 until output returns to Period t – 1: initial its natural rate. The long equilibrium at A run equilibrium is at A. A shock to aggregate supply: one more time Y π DAS2002 DAS2003 DAS2004 π2001 + ν2002 π2002 π2003 π2004 B C D π2000 = π2001 ν2002 DAS2001 A DAD Y04 Y02 Y03 Y01 Y Inflation Shock • So, we see that if a one-period inflation shock hits the economy, – inflation rises at the date the shock hits, but then returns to the unchanged long-run level, and – GDP falls at the date the shock hits, but then returns to the unchanged long-run level • What happens to the interest rates i and r? Inflation Shock Y Y Y Y it t t t* Y Yt Yt it t rt 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 Parameter values for simulations Yt 100 2.0 1.0 * t 2.0 0.25 0.5 Y 0.5 The central bank’s inflation target is 2 percent. A 1-percentage-point increase in the real interest rate reduces output demand by 1 percent of its natural level. The natural rate of interest is 2 percent. When output is 1 percent above its natural level, inflation rises by 0.25 percentage point. These values are from the Taylor Rule, which approximates the actual behavior of the Federal 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 A one-period supply shock affects output for many periods. Yt The dynamic response to a supply shock t t Because inflation expectations adjust slowly, actual inflation remains high for many periods. The dynamic response to a supply shock t rt The real interest rate takes many periods to return to its natural rate. The dynamic response to a supply shock t it The behavior of the nominal interest rate depends on that of inflation and real interest rates. A Series of Aggregate Demand Shocks • Suppose the economy is al the long-run equilibrium • Then a positive aggregated demand shock hits the economy for five successive periods (ε > 0), and then goes away (ε = 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 (νt > 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 (εt > 0), shifts right A shock to aggregate π πt + 5 G πt πt – 1 Yt + 5 Period t – 1: initial demandequilibrium at A Period t: Positive demand DASt +5 shock (ε shifts AD to the Period t +>1:0)Higher inflation Y right; output and inflation DASt +4 in t raised Periods t +inflation 2 to t + 4: rise. forint +previous 1, Higher inflation DASt +3 expectations F shifting DAS up. Inflation period raises inflation DASt +2 rises more, output falls. expectations, shifts DAS up. E Period t +rises, 5: DAS is higher output falls. DASt + 1 Inflation D due to higher inflation in C DASt -1,t preceding period, but demand shock ends and B DADPeriods returnstto initial + 6itsand higher: position. Equilibrium at G. DAS gradually shifts DADt ,t+1,…,t+4 down as inflation and A inflation expectations DADt -1, t+5 fall. The economy Y gradually recovers and Yt –1 Yt reaches the long run equilibrium at A. A 3-period shock to aggregate demand π DAS04 Y DAS03 π03 π02 C π01 π1999 = π00 DAS02 D DAS00,01 B 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. A shock to aggregate demand π DAS04 DAS05 DAS06 Y π03 π04 π05 π1999 = π00 DAS00,01 A DAD00,04,05,06 Y04Y05 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 longrun equilibrium. 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? Inflation Shock Y Y Y Y it t t t* Y Yt Yt it t rt t t * t * t Y Y t t t t • According to the monetary policy rule, an increase (decrease) in either inflation or output dictates an increase (decrease) in the real interest rate • We can do simulations for specific values of the parameters and exogenous variables 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 (ρ) The dynamic response to a demand shock t Yt The demand shock raises output for five periods. When the shock ends, output falls below its natural level, and recovers gradually. The dynamic response to a demand shock t t The demand shock causes inflation to rise. When the shock ends, inflation gradually falls toward its initial level. The dynamic response to a demand shock t rt The demand shock raises the real interest rate. After the shock ends, the real interest rate falls and approaches its initial level. The dynamic response to a demand shock t it The behavior of the nominal interest rate depends on that of the inflation and real interest rates. Stricter Monetary Policy • Suppose an economy is initially at its long-run equilibrium • Then its central bank becomes less tolerant of inflation and reduces its target inflation rate (π*) from 2% to 1% • What will be the short-run effect? • How will the economy adjust to its new longrun 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 (νt > 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 (εt > 0), shifts right A shift in monetary Y π πt – 1 = 2% πt Period t – 1: target inflation rate π* = 2%, policy initial equilibrium at A DASt -1, t DASt +1 A B C πfinal = 1% DASfinal Z DADt – 1 DADt, t + 1,… Yt Yt –1 , Yfinal Y Period t: Central bank lowers target to π* = 1%, raises real interest rate, shifts DAD leftward. Output and inflation fall. Period t + 1: The fall in πt reduced inflation expectations for t + 1, shifting DAS downward. Output rises, inflation falls. Subsequent periods: This process continues until output returns to its natural rate and inflation reaches its new target. 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 (ρ) – The effect on the nominal interest rate (i = r + π) 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 (ρ) – The nominal interest rate falls to its new and lower longrun level (i = ρ + π*) The dynamic response to a reduction in target inflation t* Yt Reducing the target inflation rate causes output to fall below its natural level for a while. Output recovers gradually. The dynamic response to a reduction in target inflation t* t Because expectations adjust slowly, it takes many periods for inflation to reach the new target. The dynamic response to a reduction in target inflation t* rt To reduce inflation, the central bank raises the real interest rate to reduce aggregate demand. The real interest rate gradually returns to its natural rate. The dynamic response to a reduction in target inflation t* it The initial increase in the real interest rate raises the nominal interest rate. As the inflation and real interest rates fall, the nominal rate 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…. APPLICATION: Output variability vs. inflation variability CASE 1: θπ is large, θY is small π A supply shock shifts DAS up. DASt DASt – 1 πt In this case, a small change in inflation has a large effect on output, so DAD is relatively flat. πt –1 DADt – 1, t Yt Yt –1 Y The shock has a large effect on output, but a small effect on inflation. APPLICATION: Output variability vs. inflation variability CASE 2: θπ is small, θY is large π DASt πt DASt – 1 In this case, a large change in inflation has only a small effect on output, so DAD is relatively steep. πt –1 DADt – 1, t Yt Yt –1 Y Now, the shock has only a small effect on output, but a big effect on inflation. 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 θπ > 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 ) Y (Yt Yt ) * t (DAD) (MP rule) If θπ > 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 ) Y (Yt Yt ) * t (DAD) (MP rule) If θπ < 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 θπ from published research: – θπ = – 0.14 from 1960-78, before Paul Volcker became Fed chairman. Inflation was high during this time, especially during the 1970s. – θπ = 0.72 during the Volcker and Greenspan years. Inflation was much lower during these years.