UNIVERSITY OF OSLO
DEPARTMENT OF ECONOMICS
Term paper in: ECON4325 – Monetary policy and business fluctuations
Handed out: Wednesday, March 21, 2007
To be delivered by: Wednesday, April 11, 2007 before 2:00 p.m.
Place of delivery: Department office, 12th floor
Further instructions:
· This term paper is compulsory. Candidates who have passed the compulsory term paper in a previous semester, does not have the right to hand in the term paper again. This is so, even if the candidate did not pass the exam.
· You must use a printed front page, which will be found at http://www.oekonomi.uio.no/info/EMNER/Forside_obl_eng.doc
· Note: The students can feel free to discuss with each other how to solve the problems, but each student is supposed to formulate her/his own answers. Only single-authored papers are accepted, and papers that for all practical purposes are identical will not be approved.
· It is of importance that the term paper is delivered by the deadline (see above). Term papers delivered after the deadline, will not be corrected.*)
· All term papers must be delivered to the place given above. You must not deliver your term paper to the course teacher or send it by e-mail.
· If the term paper is not accepted, you will be given a new attempt. If you still not succeed, you will not be permitted to take the exam in this course. You will then be withdrawn from the exam, so that this will not be an attempt.
*) If a student believes that she or he has a good cause not to meet the deadline (e.g. illness) she or he should discuss the matter with the course teacher and seek a formal extension. Normally extension will only be granted when there is a good reason backed by supporting evidence (e.g. medical certificate).
All problems should be answered. Try to answer briefly and to the point.
A Real business cycle models
(i) Explain the key differences between basic real business cycle models and traditional Keynesian models, including differences in the main assumptions and in the important mechanisms. What was the motivation for developing RBC models?
(ii) What are the effects of a permanent positive productivity shock on the economy? Explain the difference in effects between a permanent and a temporary productivity shock.
(iii) In King and Rebelo, equations
(4.5)
are described, respectively, as labour demand and labour supply. Interpret these equations, i.e. explain the right hand side variables, and explain why these variables have the postulated effect on the left-hand side variables.
(iv) Explain the rationale for Gali’s argument that “exogenous variation in technology plays a very limited role, if any, as sources of the business cycle”.
Sketch of solution
(i) Some of the key difference between RBC and traditional Keynesian models are
Traditional Keynesian models typically consist of behavioural equations, like the consumption function and an investment function. These equations are often motivated from the behaviour of households and firms, but they are not explicitly derived from optimising behaviour (utility or profit maximisation). Large empirical models of the Keynesian tradition are usually developed by use of estimated relationship on historical data. In Keynesian models, output is usually demand-determined in the short-run, with consumption-multiplier effects. Prices and inflation are often modelled with a Phillips curve. Business fluctuations are associated with fluctuations in unemployment. One motivation for the models is to have a tool for stabilization policies, to use monetary and fiscal policy to stabilize the economy.
The basic RBC model is based on the neoclassical growth model, with stochastic productivity. There is market clearing, no monetary factors, and the equilibrium is Pareto-optimal, or constrained Pareto-optimal, i.e. optimal subject to informational or institutional constraints in the economy. Thus, there is no rationale for stabilization policies.
In constructing RBC-models, one postulates utility and production functions that are consistent with a stable growth path, and key parameters are found by use of calibration, e.g. so as to ensure that first and second order moments (means, variances and co-variances) are consistent with empirical values. Some parameter values are taken from micro studies. The stochastic properties of the productivity or technology shock are usually found from the Solow residual, i.e. residuals from an aggregate production function (the variation in output that is not caused by variation in inputs). With market clearing and productivity shocks as the source of fluctuations, there is no role for separate demand shocks.
The main motivation for developing RBC models was weaknesses of the Keynesian models. There was a disconnect between micro (with optimisation) and macro (with estimated behavioural equations). RBC- proponents argued that dynamic optimising behaviour was inconsistent with invariant behavioural equations. The Lucas critique stressed the importance of deriving models from first principles. Furthermore, it was found that “business cycles are all alike”, suggesting that the main properties of aggregate fluctuations are not influenced in an important way by institutional or country-specific factors. Thus, it should be possible to construct a unified theory of the business cycle.
(ii) A permanent productivity shock will imply a new steady state of the economy where output, consumption, investment, real wages etc, increase in proportion to the rise in productivity, while labour supply (i.e. hours) is constant. This follows from the functional forms that are used in the model. The reason that hours is not affected, is that the negative wealth effect (“work less when you become richer”) cancel out with the positive substitution or wage effect (“higher real wages raises the gain in consumption from supplying another hour work”).
However, as the new steady state requires more capital, the economy does not move immediately there. At the impact, capital is below its new steady state value, implying that the marginal productivity of capital, as well as the real interest rate, is above the steady state values. The high marginal productivity of capital increases investment, and the high interest rate pushes down consumption relative to the new steady state value. The high real interest also raises labour input, in spite of the fact that real wages are below the new steady state value, as the fact that capital is below the equilibrium value implies that marginal productivity of labour is below its steady state value.
Under a temporary productivity shock, the wealth effect is smaller. Thus, labour supply is higher, which raises output, dampens real wages, and raises investment. The smaller wealth effect also implies that consumption is lower that under a permanent productivity shock, giving room for higher investment.
(iii) Equation is referred to as labour demand, as it specifies the first order condition of the firm associated with labour demand. The “hats” indicate proportionate deviation of a variable from its steady state level, and the right hand side of the equation shows the deviation of the marginal productivity of labour from its steady state level. The marginal productivity of labour is higher, the higher the productivity level (A), and the higher the capital stock is relative to the level of labour input (k – N). In optimum, the marginal product of labour is equal to the real wage.
Equationis labour supply, as it is derived from the optimal labour supply decision of the worker, where the marginal substitution between consumption and leisure is equal to the real wage. λ is the shadow price associated with the consumption-saving decision. When λ is high, the marginal utility of consumption is high, and so is the real interest rate, and the worker will raise his or her labour supply to increase consumption. A temporary higher real wage will also make the worker raise labour supply. The effect on labour supply is larger, the larger the labour supply elasticity, i.e. the lower the value of η.
(iv) On the basis of evidence from a structural VAR, Gali finds that a positive technology shock has a negative effect on labour input. To identify technology shocks, Gali imposes the long run restriction that only technology shocks could have a long run effect on labour productivity.
The negative effect of a technology shock on labour input is inconsistent with the basic RBC model with productivity as the source of output fluctuations. Stylised business fluctuation facts show that output and hours increase in booms. However, this is not consistent with a model where a positive technology shock raises output while hours fall.
B Lucas incomplete information model
(i) What is the source of output fluctuations in the Lucas incomplete information model?
(ii) Under the assumptions made in Romer 6A, output and inflation in the economy are given by
(6.32) yt = (b/(1+b)) ut
(6.33) πt = c + (b/(1+b)) ut-1 + ut/(1+b)
where yt is aggregate output, πt is inflation, c is the drift in the money stock, b is the slope-coefficient in the Lucas supply curve, and ut is a white noise shock to the money stock process.
Explain why a positive shock to the money stock gives rise to both higher output and higher inflation. Explain why in the following period, the shock only affects inflation. .
(iii) Assume that producers instead have adaptive expectations with respect to the price level, i.e. that producers’ expected price E[pt] = pt-1. Derive aggregate output and inflation as functions of the money stock mt and the lagged price level. Within this model, can the monetary policy maker affect output and inflation?
(iv) Discuss the plausibility of the assumptions made in (iii). Are there any circumstances under which this postulated expectation formation is plausible?
Sketch of solution
(i) Source of output fluctuations: Output depends on relative prices. If a producer faces a higher relative price, he or she will raise production. If a positive shock to the money stock takes place, aggregate demand will increase, pushing up all prices. Producers, however, do not know that all prices increase, as they only observe their own price. Thus, they believe that their relative price has increased, and consequently they increase production.
(ii) A positive shock to money has a positive effect on both output and inflation, as explained in (i) above. In the next period, producers know the effect on aggregate prices of the money shock in the previous period, and thus it does not lead them to make errors as to relative prices. Thus, output will be equal to the steady state value in the next period.
In contrast, as producers reduce their supply, aggregate prices continue to increase in the next period, implying that a positive shock to the money stock raises inflation in two consecutive periods, and not only in the first period.
(iii) Using the same method as in Romer, the aggregate supply curve is now (corresponds to 6.21)
(1) yt = b( pt – pt-1)
Aggregate demand is
(2) yt = mt - pt
Imposing supply equal to demand, we obtain
(3) mt - pt = b( pt – pt-1)
which solves for
(4) pt = 1/(1+b) mt + b/(1+b)pt-1
From (4), we obtain
(5) πt = pt – pt-1 = 1/(1+b)( mt - pt-1)
and
(6) yt = mt – pt = b/(1+b)( mt - pt-1)
We observe that in this model, the monetary policy maker can increase output and inflation by increasing the money stock above the price level of the previous period.
(iv) The postulated expectation formation is not consistent with rational expectations. Thus, if the policy maker tries to exploit this expectation formation, by raising the money stock so as to increase output, producers will observe that they make errors. If the policy maker does this systematically, the expectation formation will adapt, and rational expectations is more realistic.
However, in an environment where the policy makers keep the money stock stable, the postulated expectation mechanism is not systematically wrong. Then it might also be realistic, and it would leave some room for temporary exploitation by the policy maker.
C Time-inconsistency
Suppose that the preferences of the government are represented by the following loss
function:
1)
where πt is inflation and yt is output, measured as deviation from potential output. y* > 0 is the government’s output target.
(i) Why could the government (society) have a target for output that exceeds potential output?
(ii) The inflationary bias is defined as. Derive optimal monetary policy under discretion and show how the inflationary bias depends on the output target y*.
(iii) Show how the inflationary bias can be removed by adding a term cπt to the loss function with an appropriately specified coefficient c. How could such a term be interpreted?
Sketch of solution
Ad (i) Market imperfections (unions, monopolists etc) can give lower output and employment than what is socially optimal
Ad (ii) F.O.C:
2)
Take the expectation at time t-1:
3)
=> . (Note that )
Bias = where we have used that .
Solution for inflation:
4)
Ad (iii). New F.O.C:
5)
Take the expectations at time t-1:
=>
By specifying , the bias will be removed.
How can the term be interpreted? The term implies that the central bank receives an additional punishment if inflation is above the target. In the quadratic loss function (0.1), the marginal disutility of inflation above the target, measured at the point where inflation is equal to the target (i.e. dL(π*, . )/dπ ) is equal to zero, thus the central bank incurs essentially no utility loss for a marginal deviation from target. When adding a linear term in inflation to the loss function, the marginal disutility of higher inflation is strictly positive also measured at the point where inflation is equal to target, and one can avoid the inflation bias.