1. Introduction
New Keynesian Economics is well-known in an academic area nowadays. But it is not necessarily understood in a full meaning especially about its macroeconomic implication. This paper tries to explain its roots, formation and background theoretically. Then this paper proceeds to interpret this decades’ condition of Japanese economy in the view point of new Keynesian macroeconomic theory, which will give us some implications and suggestions to solve the difficult problem around Japanese economy.
New Keynesian macroeconomic model is consisted of three equations. The first one is new Keynesian Phillips curve. As is understood well, the curve explains the trade-off between unemployment rate and inflation rate. Unemployment rate can be translated into GDP gap, which means the difference from the normal level of potential GDP. In new Keynesian version, thus this curve is the trade-off between GDP gap and inflation rate.
An Interpretation of the New Keynesian Macroeconomics for Japanese Economy
in the Recent Economic Condition
Yoshihiro Yamazaki
＊＊Faculty of Economics, Fukuoka University, Fukuoka, Japan
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The second element of new Keynesian macroeconomics is new Keynesian IS curve. This is roughly the same as ordinary IS curve, which explains the balance between interest rate and equilibrium GDP. This GDP is its gap from normal one here, too. And we will show the possibility of a positive inclination of this curve.
The third element is Taylor rule. New Keynesian replaces ordinary LM curve with this one. Taylor [1993] proposed a financial policy rule investigating practices by central banks. Taylor’s understanding was that central banks arrange an interest rate according to changes of GDP gap and inflation rate. Taylor intended to coordinate the debate between discretion policy and rule-based policy.
2. Sticky Price and New Keynesian Phillips Curve
New Keynesian Phillips curve has an important difference from the ordinary one.
The ordinary curve also includes an expectation term of inflation rate but it is last year’s expectation of this year’s rate. On the contrary, the same term is this year’s expectation of next year’s inflation rate in new Keynesian case.
Here 0＜β!1, μ＞0, γ＞0. πt and xt are respectively inflation rate and GDP gap. eπtis zero mean and serially uncorrelated supply shock.
This characteristic of new Keynesian Phillips curve comes from micro foundation of new Keynesian economics. New Keynesian economics supposes that firms are price makers and that because it costs some to change prices, the price level becomes sticky. In short, their model is imperfect competition with sticky prices.
Blanchard & Kiyotaki [1987] is a new Keynesian general equilibrium model but
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it doesn’t have the assumption of adjustment cost of prices. The firms can change prices into the optimal level without any burden. Therefore the prices only depend on this year’s variables.
On the other hand, Calvo [1983] and Yun [1996] introduced the sticky price assumption into the model. As there is some adjustment cost in changing prices, firms can only change prices at some probability. Or though the same meaning, some firms can change prices this year but the others cannot.
If only 1−ρ firms can change prices, a single firm i face the problem as follows ;
Here is firm i’s demand function, where, Yt, Pt are total production of the industry and general price level respectively. δ,θare subjective discount factor and price elasticity of demand.
Firms produce according to production function , where K is capital and L is labor. W and r are respectively wage rate and profit rate. The general price level is an average of new price Z of 1−ρfirms and old price P.
The optimal condition of the firms turned to be as follows ;
Here ULC means unit labor cost that is proportional to marginal cost of production in Cobb=Douglas production function.
An Interpretation of the New Keynesian Macroeconomics
for Japanese Economy in the Recent Economic Condition（Yamazaki） −１４１−
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This condition means that firms fixed this year’s price so as to be equal to the weighted average of marked-up marginal costs in the future. A firm may not change the price at some points in the future because of adjustment cost. Thus if it maximize only this year’s profit, the firm may lose future profits. So they have to decide this year’s price in comparison with the future prices. Such a feature of this model makes the expectation in new Keynesian Philips curve a forward looking one.
A Philips curve can also be derived from neo-classical models. Fisher [1977]
assumed thatρfirms can set the optimal price while 1−ρfirms have to follow the price expected by themselves last year. Then the Phillips curve includes the expectation term but it is last year’s expectation of this year’s price not this year’s expectation of next year’s price.
3. New Keynesian IS Curve and Interest Rates
We shall consider the representative household to derive new Keynesian IS curve. It maximizes the present value of utility flow in the future.
In maximizing utility, the household has to follow the budget constraint ;
Here A, C, I, r are asset, consumption, labor income and profit rate respectively.
The optimal condition of the household is written in the Euler equation ;
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Approximating marginal utility by , we obtain the relation as follows ;
Here and . σis called the coefficient of relative risk aversion and is time preference rate.
(The deriving process is as follows ;
Here we neglect a very small term.
Because , we obtain the above equation. A natural
logarithm is an approximation of growth ratio.)
For simplicity, there is no physical capital and net financial assets offset each other. Then GDP is equal to consumption.
An Interpretation of the New Keynesian Macroeconomics
for Japanese Economy in the Recent Economic Condition（Yamazaki） −１４３−
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The right hand of the above equation is therefore the difference between the expectation of next year’s GDP and this year’s actual GDP. So by replacing them with GDP gap, we obtain new Keynesian IS curve.
Here i is a nominal interest rate and calculated through Fisher equation .
Normally σ＞0, but if people are risk lovers, the higher interest rate become, the more they will spend.
4. The Meaning of Taylor Rule
Finally, the standard Taylor rule is like this.
Hereπ＊is targeted inflation rate andψ＞0, ω＞0. If actual inflation rate is equal to targeted one and there is no GDP gap, a central bank fixes the nominal interest rate to the level of the time preference plus an appropriate inflation rate.
When inflation is too rapid, the central bank raises the policy rate. In the case of economic recession, the policy rate will be cut because GDP gap is minus.
Taylor [1993] proposed this formula investigating the actual policy making process of the Fed, the United States’ central bank. He intended to fix the conflict between rule and discretion in the economic policy area.
Old Keynesians conducted discretional policies in the 1960s and 1970s. They recommended reducing an interest rate in the recession and raising it in the boom.
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But neo-classical economists have attacked this discretional policy style since the late 1970s. Lucas [1975] pointed the possibility that economic policies may change structural parameters of an economy. Then the estimation of policy effects comes to be incredible. This proposal is called Lucas critique.
Soon after that, Kydland & Prescott [1977] proposed the problem of time inconsistency. They told that because people plan to allocate their labor and production among the series of time periods, policy makings without consideration on such time allocation must turn out to be failures. Thus among the academic economists, the belief that rules are much better than discretion came to a common sense.
Taylor, however, wrote that “[d] spite the emphasis on policy rules in recent macroeconomic research, the notion of a policy rule has not become a common way to think about policy in practice. Policymakers do not, and are not evidently about to, follow policy rules mechanically. (Ibid., 196.)”
Taylor, thus, broadened the definition of “policy rules” to find the useful formula of policy practice. He wrote that “[a] policy rule can be implemented and operated more informally by policymakers who recognize the general instrument responses that underlie the policy rule, but who also recognize that operating the rule requires judgment and cannot be done by computer. (Ibid., 198.)”
Nowadays, Taylor rule seems to be adopted by almost all the central bankers of advanced countries. Annual economic report of Japanese government also wrote like this about 2005-to-2006 monetary policy.
Incidentally, there is what is called the Taylor Rule as one of the methods for setting interest rates. It is a monetary policy rule to derive a policy rate
An Interpretation of the New Keynesian Macroeconomics
for Japanese Economy in the Recent Economic Condition（Yamazaki） −１４５−
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(uncollateralized overnight call rate, in the case of Japan) in accordance with economic conditions. Specifically, it is a rule to derive a policy interest rate in accordance with the magnitude of deviation of the current inflation rate from the long-term target rate and of the supply-demand gap from the equilibrium value. We estimated the policy rate derived from the Taylor Rule based on the inflation rate of 0〜2％presented as an “understanding of medium- to long-term price stability.” Specifically, assuming target inflation rates are from 0 to 2 percent, we estimated policy interest rates derived from the rule by using consumer price indices and the supply-demand gap estimated by the Cabinet Office. The estimation results show that the current interest rate level is in positive territory. With regard to the interpretation of the interest-rate level derived from the estimation, there are several points to keep in mind, such as supply-demand gap measuring errors and a lag in the ripple effects of the monetary policy. There are problems in deriving monetary policy management patterns on the basis of a mechanical rule. It is extremely important to have a system to stabilize economic activities by enhancing the transparency of monetary policy and thereby facilitating private sector’s expectation formation. From this perspective, it is hoped that the Bank of Japan and the private sector will have proper communications under the “New Framework for the Conduct of Monetary Policy.”
Here the cabinet office described objectively the fact that the BOJ has adopted Taylor rule and that the central bank thinks much of people’s confidence to the policy.
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5. Conclusion
As now we investigate the basic structure of new Keynesian macroeconomics, we shall proceed to interpret Japanese economic condition from the view point of new Keynesian.
Firstly, in Japan the price level continued to go down these years. Because of the rise of oil price, this deflation seemed to stop finally this year. But world financial crisis and the following recession will put Japanese economy in the deflation again. This deflationary tendency that we can see in Japanese economy can be ascribe to the fact that firms’ control power over price becomes weaker.
This is in turn because the global competition goes stronger. We can explain it as θ’s increasing from the view point of new Keynesian model.
Secondly, during what they called “lost decade” of Japanese economy, the interest rates were very low. But Japanese economy stayed in the bad condition.
New Keynesian IS curve teaches us that during the period, people’s risk aversion σmight be so large.
Thirdly, Taylor rule has been adopted by the Bank of Japan as a monetary policy rule. Anyway, the rule is the central bankers’ favorite and the BOJ also has many new Keynesian researchers. In an economic recovery for these years, the BOJ returned its policy target to a short-term interest rate from the amount of legal reserve. But the financial crisis that started in the second half of this year may force the central bank to go back to another quantitative easing policy.
Reference
Blanchard, O. and N. Kiyotaki, 1987, ‘Monopolistic Competition and the Effects of Aggregate Demand,’American Economic Review 77, 646‐66.
An Interpretation of the New Keynesian Macroeconomics
for Japanese Economy in the Recent Economic Condition（Yamazaki） −１４７−
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Calvo, G. A., 1983, ‘Staggered Prices in a Utility Maximizing Framework,’Journal of Monetary Economics12, 383‐98.
Fischer, S., 1977, ‘Long Term Contracts, Rational Expectations and the Optimal Money Supply Rules,’Journal of Political Economy85, 191‐205.
Japanese Cabinet Office, 2006,Annual Report on the Japanese Economy and Public Finance.
Kydland, F. & Prescott, E. C., 1977, ‘Rules rather than Discretion : the Inconsistency of Optimal Plans,’Journal of Political Economy85, 473‐92.
Lucas, R. E., 1975, ‘An Equilibrium Model of Business Cycle,’Journal of Political Economy 83, 1295‐328.
Taylor, J. B., 1993, ‘Discretion versus Policy Rules in Practice,’Carnegie-Rochester Conference Series on Public Policy 39, 195‐214.
Yun, T., 1996, ‘Nominal Price Rigidity, Money Supply Endogeneity and Business Cycles,’Journal of Monetary Economics37, 345‐70.
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