Inflation, Output, and Nominal Money. Growth

Transcription

1 Money Money Department of Economics, University of Vienna May 25 th, 2011

2 Money The AS-AD model dealt with the relation between output and the price level In this chapter we extend the AS-AD model to examine three variables: output growth, the unemployment rate, and inflation In order to do this, we will need a dynamic model (i.e. our variables will depend on time) For that purpose we use three relations: the Phillips curve, Okun s law and a particular form of the aggregate demand relation

3 Motivation Money We can derive a relationship between the unemployment rate and output growth by calculating the growth rate of real GDP from period t 1 to period t: Output growth is given by g Y,t = Y t Y t 1 Y t 1 = Y t Y t 1 1 Because of Y t = A t N t we can write g Y,t = A tn t A t 1 N t 1 1

4 Motivation We also know that Therefore we get u t = 1 N t L t N t = L t (1 u t ) g Y,t = A t L t (1 u t ) A t 1 L t 1 (1 u t 1 ) 1 = (1 + g A)(1 + g L )(1 u t ) (1 u t 1 ) 1 Money For small values of u t, u t 1, g A and g L we can use an approximation to get u t u t 1 = [g Y,t (g A + g L )] (1)

5 Interpretation Money The sum g A + g L, i.e. the sum of the growth rate of productivity and the growth rate of the labor force, is called the normal growth rate (ḡ Y ) Equation (1) states that output growth above (below) normal implies a decrease (increase) in the unemployment rate Intuition: Production growth will only lead to a lower unemployment rate if it can not be accomplished through productivity growth of the current workers or a growth of the labor force (which means that for a given unemployment rate a higher number of people are working).

6 Traditional Form In the 1960s, Arthur Okun showed that the actual relation is a little different Using U.S. data he concluded that the relation has the following form u t u t 1 = β(g Y,t ḡ Y ) (2) The main difference between (1) and (2) is the parameter β which is called Okun s coefficient This coefficient is usually assumed to be between zero and one, i.e. 0 < β < 1 This implies that if output growth exceeds the normal growth rate by x then the unemployment rate does not decrease by the same amount, due to the factor β Money

7 Implications There are two main reasons for this difference: To a certain extent, the number of workers a firm uses is independent of its production (e.g. accounting department is also needed when production is rather low; since training new workers is costly, firms tend to keep the already trained workers through economic downturns or let them work overtime when production is very high,...) Jobs created by output growth above normal are not only filled with unemployed workers but also by workers previously classified as out of the labor force; in addition, some of the latter are encouraged to look for a job and get unemployed opposing effects on the unemployment rate and therefore a smaller change in u t Money

8 The Reformulation The aggregate demand relation is given by ( ) Mt Y t = f, G t, T t P t In the following we assume G t and T t to be constant over time so that we can neglect them From the IS-LM model we know that an increase in the real money supply leads to a decrease in the interest rate and consequently to an increase in the demand for goods (investment) and therefore to an increase in output Thus, output increases with the real money supply and we assume that this relation is linear Money Y t = γ M t P t

9 The Reformulation Finally we transform the aggregate demand relation into a relation between growth rates For this purpose, note that 1+g Y,t = Y t Y t 1 = γ Mt P t γ M t 1 P t 1 As a result, we finally get = (1 + g M,t) (1 + π t ) 1+g M,t π t Money g Y,t = g M,t π t (3) Equation (3) states that if nominal money growth exceeds (is less than) inflation, real money growth is positive (negative) and so output growth is positive (negative)

10 Money : u t u t 1 = β(g Y,t ḡ Y ) Phillips Curve: π t π t 1 = α(u t u n ) AD : g Y,t = g M,t π t

11 Continued Money The exogenous variables of this system are u n and ḡ Y, which are determined by structural parameters of the economy, as well as g M,t, which is choosen by the central bank The variables u t 1 and π t 1 are predetermined, i.e. they are given from the previous period So in period t, this system of three linear equations can be used to determine the solution for g Y,t, u t and π t simultaneously

12 Effects of a Decrease in Money An Example Money In order to analyze the short and the medium run effects of a decrease in nominal money growth, assume that the economy is in a medium run equilibrium in period t 1. In particular g Y,t 1 = ḡ Y = 3%, u t 1 = u n = 6%, g M,t 1 = 8% and thus π t 1 = 5%. The central bank decreases nominal money growth in period t to g M,t = 6% and leaves it at that rate thereafter The effects of this policy are depicted in the graph on the following slide

13 Effects of a Decrease in Money Graphical Illustration Money Figure: Development of endogenous variables u, π and g Y

14 Effects of a Decrease in Money An Example Money A decrease in nominal money growth decreases output growth and increases the unemployment rate in the short run In the medium run they both return to their natural rates while inflation decreases and remains at a lower level The movements of output growth and the unemployment rate between the short and the medium run depend on the path of monetary policy These results are natural extensions of the results of the AS-AD model: a change in the nominal supply of money did not affect output or unemployment in the medium run, but changed the price level

15 Money Assume that there is consensus among policy makers that inflation has to be reduced, i.e. disinflationary measures have to be implemented From the previous example we know that reducing inflation requires lower nominal money growth and comes at the expense of higher unemployment (in the short run) This fact is already clear from the Phillips curve relation π t π t 1 = α(u t u n ) A decrease in inflation is obtained via an unemployment rate above the natural rate

16 Money The Phillips curve relation has another interesting implication: lowering inflation to a particular target can either be achieved very quickly (if the unemployment rate is much higher than the natural rate for a short period of time) or more slowly (if the unemployment rate is just above the natural rate for a long time period) In either case, however, the total number of additional unemployed workers necessary to decrease inflation to that particular level is the same This traditional approach to disinflation was challenged in the following way

17 The economist Robert Lucas pointed out that the way wage setters form their expectations about future inflation is likely to change if (inflation) policy changes In particular, if policy makers are committed to reduce inflation to a certain rate then we should not assume that workers set their expectations according to π e t = π t 1 In deriving the relation between the Phillips curve and the natural rate of unemployment, however, we did just that Money Assuming instead no specific way in which wage setters form their expectations we can write the Phillips curve as π t = π e t α(u t u n ) (4)

18 Equation (4) indicates that a decrease in inflation can be achieved by an unemployment rate u t above u n (traditional disinflation approach) or by a decrease in π e t or both In other words, Lucas emphasised that disinflation could be achieved with a lower increase in the unemployment rate than suggested by the traditional approach, given that wage setters believe in the lower inflation target and as a result lower their expectation about future inflation The crucial point in this respect is the credibility of monetary policy The Lucas critique also indicates the large role of expectations in an economy Money

19 Money The presence of nominal rigidities, meaning that wages and prices are set in nominal terms for some time and are typically not readjusted when there is a change in policy, challenges the implications of the Lucas critique Stanley Fischer argued that despite credibility, a rapid decrease in nominal money growth would lead to higher unemployment, because it would take some time before changes in inflation expectations would become effective As a result, measures to reduce inflation should be announced sufficiently in advance to allow wage setters to take into account the change in policy

20 Money The extended AS-AD model helps us to analyse the relation between output growth, the unemployment rate and inflation In particular, the model indicates that a decrease in nominal money growth in order to decrease inflation temporarily leads to lower output growth and a higher rate of unemployment; in the medium run they return to their natural rates and inflation stabilises at a lower level