MANKIW'S MACROECONOMICS MODULES ® MANKIW'S MACROECONOMICS MODULES CHAPTER 14 A Dynamic Model of Aggregate Demand And Aggregate Supply A PowerPointTutorial To Accompany MACROECONOMICS, 7th. Edition N. Gregory Mankiw Tutorial written by: Mannig J. Simidian B.A. in Economics with Distinction, Duke University M.P.A., Harvard University Kennedy School of Government M.B.A., Massachusetts Institute of Technology (MIT) Sloan School of Management

Elements of the Model Elements of the Model Elements of the Model Although the dynamic AD-AS model is new to the reader, most of its components are not. Compared to the models in previous chapters, the dynamic AD-AS model is closer to those studied by economics at the research frontier. We need to introduce one piece of notation: throughout this chapter, a subscript t on a variable represents time. For example, Yt represents GDP in time period t. Yt-t represents national income in period t-1 and Yt+1 represents national income in period t+1. This new notation allows us to keep track of variables as they change over time. Let’s now look at the five equations that make up the dynamic AD-AS model.

Output: The Demand for Goods and Services The demand for goods and services is given by the equation: Yt = Y – a (rt – r) + et Random demand shock Total output of goods and services Parameters >0 Real interest rate Natural rate of output Key feature: the negative relationship between the real interest rate r and the demand for goods and services. Also, this equation explicates that as long-run growth makes the economy richer, the demand for goods and services grows proportionally.

The Real Interest Rate: The Fisher Equation The real interest rate in this dynamic model rt is the nominal interest rate it is the nominal interest rate it minus the expected rate of future inflation Etpt+1: rt = it - Etpt+1 Nominal interest rate Expectation formed in period t of inflation in period t + 1 Ex ante real interest rate: the real interest rate that people anticipate based on their expectation of inflation Note– on notation and timing convention: The variables rt and it are in interest rates that prevail at time t and therefore represent a rate of return between periods t and t+1.

Inflation: The Phillips Curve Inflation in this economy is determined by a conventional Phillips curve augmented to include roles for expected inflation and exogenous supply shocks. The equation for inflation is: pt = Et-1pt + j (Yt – Yt) + ut Inflation depends on A parameter > 0 tells how much Inflation responds when output Fluctuates around its natural level Expected inflation This gap measures the state of the business cycle; the deviation of output from its natural level (Yt – Yt) Supply shock in a given period which could be positive of negative.

Expected Inflation: Adaptive Expectations Expected inflation plays a part in both the Phillips curve equation for inflation and the Fisher equation relating nominal and real interest rates. To keep the dynamic AD-AS model simple, as assume that people form their expectations of inflation based on the inflation they have recently observed. That is, people expect prices to continue rising at the same rate they have been rising. This is sometimes called the assumption of adaptive expectations. It can be written as: Et-1pt= pt-1 When forecasting in period t-1 what inflation rate will prevail in prevail in period t, people simply look at inflation in period t-1 and extrapolate it forward. The same assumption applies in every period. Thus once inflation is observed in period t, people will expect that rate to continue. Therefore, Et+1pt= pt

The Nominal Interest Rate: The Monetary Policy Rule The final equation is the one for monetary policy. We assume that the central banks sets a target for the nominal interest rate it based on inflation and output using this rule: it = pt + r + qp(pt – pt*) +qY(Yt – Yt) This is the central bank’s target for the inflation rate They are >0 and indicate how much the central bank Allows the interest rate target to respond to Fluctuations in inflation and output Natural rate of interest Recall that the real interest rate, rather than the nominal interest rate, influences the demand for goods and services. So, while the central bank sets a target for the nominal interest rate, the bank’s influence is via the real interest rate.

Interest rate or the Money Supply? The main advantage of using the interest rate, rather than the money supply, as the policy instrument AD-AS model is that it is more realistic. Today most central banks, including the Federal Reserve, set a short-term target for the nominal interest rate. Keep in mind that hitting that target requires adjustments in the money supply. So, when a central bank decides to change the interest, it is also committing itself to adjust the money supply accordingly.

Taylor rule Economist, John Taylor has proposed a simple rule for the federal funds rate: Nominal Federal Funds Rate = Inflation + 2.0 + 0.5 (Inflation – 2.0) – 0.5 (GDP gap) The GDP gap is the percentage shortfall of real GDP from an estimate of its natural level. The Taylor Rule has the real federal funds rate— the nominal rate minus inflation responding to inflation and the GDP gap. According to this rule, the real federal funds rate equals 2 percent when inflation is 2 percent and GDP is at its natural rate.

Solving the Dynamic AD-AS Model The previous 5 equations we went over on the last few slides: The Demand for Goods and Services, The Fisher Equation, The Phillips Curve, Adaptive Expectations, The Monetary Policy Rule determine the Model’s five endogenous variables: output, the real interest rate, inflation and the nominal interest rate. We are almost ready to put these pieces together to see how various shocks to the economy influences the paths of these variables over time. Before doing so, however, we need to establish the starting point for our analysis: the economy’s long-run equilibrium.

The Long-Run Equilibrium The long-run equilibrium represents the normal state around which the economy fluctuates. It occurs when there are no shocks and inflation has stabilized. In words, the long-run equilibrium is described as follows: Output and the real interest rate are at their natural values, inflation and expected inflation are at the target rate of inflation, and the nominal interest rate equals the natural rate of interest plus target inflation. The long-run equilibrium is described as follows: Output and the real interest rate are at their natural values, inflation and expected inflation are at the target rate of inflation, and the nominal interest rate equals the natural rate of interest plus target inflation. The long-run equilibrium of this model two related principles: the classic dichotomy and monetary neutrality. Continue to understand this on the next slide….

The Long-Run Equilibrium Equations Algebra applied to the previous five equations can be used to verify these long-run values: Yt = Yt rt = r pt = pt* Etpt+1 = pt*

Recall that the classical dichotomy is the separation and monetary neutrality. Recall that the classical dichotomy is the separation of real from nominal variables, and monetary neutrality is the property According to which monetary policy does not influence real variables. The equations on the previous slide immediately show that the central bank’s inflation target pt* influences only inflation pt, expected inflation Etpt+1, and the nominal interest rate it. If the central bank raises its inflation target, inflation, expected inflation, and the nominal interest rate all increase by the same amount. The real variables– output Yt and the real interest rate do not depend on monetary policy. In these ways, the long-run equilibrium of the dynamic AD-AS model mirrors the Classical models we examined in Chapters 3 – 8.

The Dynamic Aggregate-Supply Curve Inflation, pt The dynamic AS curve (DASt) shows a positive relationship between output Yt and inflation pt. Its upward slope reflects the Phillips curve relationship: other things equals, high levels of economic activity are associated with high inflation. The DAS curve is drawn for given values of past inflation pt-1, the Natural level of output Yt , and the supply shock ut. When these variables change, the curve shifts. DASt Income, Output, Yt

The Dynamic Aggregate-Demand Curve The dynamic AD curve (DADt) shows a negative relationship between output Yt and inflation pt. Its downward slope reflects monetary policy and the demand for goods and services. A high level of inflation causes the Central bank to raise nominal and real interest rates, which in turn reduces the demand for goods and services. The dynamic AD curve is drawn for given Values of the natural level of Output Yt , the inflation target pt* and the demand shock et. When These exogenous variables shift, the curve shifts. Inflation, pt DADt Income, Output, Yt

The Short-run Equilibrium Inflation, pt DADt This equilibrium determines the inflation rate and the level of output that prevail in Period t. This diagram shows that the equilibrium falls just short of the economy’s natural level of output Yt. Short-run Equilibrium DASt Yt Income, Output, Yt

An Increase in the Natural Level of Output If the natural level of output Yt increases, both the dynamic aggregate-demand curve and the dynamic aggregate-supply curve shift to the right by the same amount. Output Yt, increases but inflation remains the same. Inflation, pt DADt Stable Inflation DASt Growth in Output Yt Yt+1 Income, Output, Yt

A Supply Shock Inflation, pt DASt DADall DASt+1 B DASt-1 C A Yall A supply shock in period t shifts the dynamic aggregate- supply curve upward from DASt-1 to DASt. The DAS curve is unchanged. The economy’s short-run equilibrium moves from point A to point B. inflation rises and output falls. In the subsequent period (t+1), the DAS curve shifts to DAS t+1 and the economy moves to point C. The supply shock has Returned to its normal value of zero, but inflation expectations remain high. As a result, the economy returns only gradually to its initial equilibrium, point A. DASt DADall DASt+1 B DASt-1 C A Yall Income, Output, Yt

See Figure 14-8 in the text for Mankiw’s A Demand Shock Inflation, pt DASt+4 DADt…t+4 DASt+3 DADt…t+5 See Figure 14-8 in the text for Mankiw’s terrific explanation. DASt+2 DASt+1 DASt-1,1 Income, Output, Yt Yall

Key Concepts of Chapter 14 Taylor rule Taylor principle