Optimizing Central Bank Operating - Assignment Example

Macro economics Macroeconomics Submitted Submitted by: 7th March 2009 !a) What has been deduced is that a compromise between credibility and flexibility, Rogoff (1985) suggested that the government should appoint a "conservative" central banker, that is, a central Banker with the following preferences: (1.12) cb (*) 2 cb * 2t t t = 1 [+ (y - y)], L 2 π −π λ where cob is the central bankers subjective weight attached to output stability, λcb < λ, That is, the central bankers weight on output is smaller than the societys weight. It can be explained as follows: Reducing BC marginally from the point BC = b Gives a first-order (“large”) gain in terms of lower average inflation and a second order (“Small”) loss in terms of reduced output stability. Increasing bc marginally from the point bc = 0 gives a first-order gain in terms of increased output stability and a second-order loss in terms of higher average inflation. Thus, the optimal bc must lie between zero and b. According to Lehmann (1992, he) showed that the outcome can be further improved if the government complements the appointment of a "conservative" central banker with an option to Override the central banker at a fixed cost. The rationale is that delegating the conduct Of monetary policy to a "conservative" central banker is costly for the society if large Shocks occur. Thus, the government will pay the price of overriding if large shocks Occur and set monetary policy at its own discretion. The central banker dislikes being overridden and pays attention to the governments preferences when responding to Large shocks. In equilibrium, the central banker is never overridden. Optimal contracts Although improving the discretionary equilibrium, the reputational and delegation Solutions to the time-inconsistency problem do not provide the second-best Equilibrium. In order to achieve the second-best equilibrium, various contracting Solutions have been considered. The relationship between the government and the Central banker may be considered a "principal-agent" problem. The government (the "Principal") delegates the conduct of monetary policy to a central banker (the "Agent") with certain incentives. The government can affect the incentives of the Central banker by specifying a contract between the central banker and the Government. Walsh (1995) and Persson and Tabellini (1993) showed that the second-best Equilibrium can be achieved by offering a linear inflation contract to a central Banker with the same preferences over inflation and output as the government. The Central bankers loss function may then be written as (1.13) cb ( *)2 * 2 t t t t = 1 [ + ( y - y ) ] + c , L 2 π −π λ πIt can easily be shown that the optimal policy is achieved if c = λγy*, i.e. the marginal penalty for generating inflation is equal to the inflationary bias under a discretionary policy. An alternative, although mathematically equivalent, way of achieving the secondbest equilibrium has been suggested by Svensson (1997). Instead of offering the central banker a linear inflation contract, the government can assign the loss function (1.14) g 2 * 2 t t t = 1 [( - ) + ( y - y ) ] L 2 π π λ to the central banker, where πg is an inflation target specified by the government. The central banker is assumed to be held accountable for minimizing the loss. The optimal policy is achieved if the inflation target is specified so that πg = π* -λγy*. Thus, the inflation target is "conservative", which means that the target level is below the socially optimal rate of inflation. b) In broad terms, the change which has come about in the specification of inflation targeting regimes comes from the recognition that if the inflation target is specified narrowly and the time horizon over which it must be achieved is tight, then the effort to keep the actual inflation rate constantly within a narrow band will involve quite a bit of short-term variation of the interest rate lever (and, consequentially, the exchange rate), and policy will be jerking output around disruptively, probably unnecessarily. Central banks may regard their sole objective as inflation, but it seems pretty clear that the community’s wishes (their objective function) has output in there as well. Any central bank which achieves its inflation objective but damages output in a way unacceptable to the community will not keep its mandate for long. It is the recognition of this point which has produced a voluminous discussion and academic literature, which basically asks the question - what is the right trade-off between rigid adherence, moment by moment, to the inflation target (on the one hand) and a steady path of output (on the other). On the basis that this rate of inflation is not disruptive, to accept that some of the most central and basic prices (principally wages) will rise faster than this .There is, of course, also the very substantial danger that a rise in non-tradeable prices faster than the target inflation rate will trigger an asset boom, particularly in the classic non-traded asset of real estate property. There is also the issue that, compared with the situation before the capital inflow and appreciation of the exchange rate, interest rates will have to fall: we know that the extra capital inflows are putting pressure on domestic asset prices, and it might well be asked whether this is an appropriate time to be easing domestic interest rates - which seems to be the implication of a simple reading of an inflation targeting regime. The problem is a familiar one, faced during the first half of the 1990s. That is, that there are very large and increasing capital inflows, which put continuing upward pressure on the exchange rate. Following the reasoning I have outlined so far, the proper response to this is to allow the exchange rate to appreciate. To the extent that this is a long-term or structural change, the inflation targeting framework would allow the appreciation to be reflected in inflation, to the extent that it meant that non-traded (domestic) prices would rise faster than the target. On most counts, this is o.k. - it is proper that relative price between tradeables and non-tradeables changes (in order to encourage the current account deficit that is the counterpart of the financial capital inflows). C) a) i ) The introduction of a lagged output gap in this equation is important for comparing inflation and price-level targeting. Conceptually, the lag will be introduced any time friction prevents instantaneous and complete adjustment of output to unexpected changes in the price level. The second equation explains monetary growth. In other words, what the central bank does. Here, they react to offset the output gap (but with a lag), but they do so imperfectly, hence the presence of the shock. The last equation simply says that inflation is driven by monetary growth. The first order conditions for optimality may be written as: The equations in (4) are orthogonality conditions involving all the deep parameters describing the preferences of the central banker π*, δ, λ, and only one parameter coming from the structure of the economy, αy. By combining equations (3) and (2) and substituting into (4), obtain the solution. C) Formally, the output gap is the difference between the economy’s actual output and potential output,with the latter being the level of production consistent with existing labor, capital and technology. Potential output can also be viewed as the level of demand that does not put pressure on inflation in either direction. A positive output gap, by convention, is referred to as excess demand while a negative output gap is referred to as excess supply. There are several key issues surrounding the output gap. One—which is not addressed in this paper—is related to the value of λ in the above model, i.e. whether or not λ=0. Conventional wisdom states that the appropriate loss function both involves stabilizing inflation around an inflation target and stabilizing the real economy, represented by the output gap. Hence λ>0 is the appropriate condition. While the desirability of incorporating the output gap in the BSP’s objective function can be evaluated both analytically and empirically, such an exercise is left for future studies. In the above framework, optimal behavior is translated into a precommtiment policy or interest rate rule represented by equation (5). Recently, it has been argued that a fully optimizing central bank operating in a discretionary policy environment achieves better social outcomes if it focuses on inflation on output gap changes rather than the level of the gap (Walsh, 2001). The change in output gap is equal to output growth minus growth in potential. Lastly, assuming that the output gap is found to be significant in determining inflation, the central bank would still be unable to perfectly distinguish between cyclical changes in output and changes in the trend component—which is the level of potential output. This issue is closely related to the accuracy of output gap measurements. Even if errors are small, these will accumulate over time and this would affect the accuracy of its inflation forecasts and also the reliability of its reaction function. For example, it has been argued that misguided monetary policy in the US that resulted from lack of recognition of shifts in potential output since 1965 was the primary cause of the great inflation in the 1970s. Reference Hanish C. Lodhia (2005) "The Irrationality of Rational Expectations - An Exploration into Economic Fallacy". 1st Edition, Warwick University Press, UK. John F. Muth (1961) "Rational Expectations and the Theory of Price Movements" reprinted in The new classical macroeconomics. Volume 1. (1992): 3-23 (International Library of Critical Writings in Economics, vol. 19. Aldershot, UK: Elgar. Read More