Monday, June 23, 2008

Exercise in Dynamic Macroeconomics

If you want to study modern dynamic macroeconomics, see it.
The version of international macro is here. These might be good exercise.

Thursday, June 19, 2008

最低賃金 (Hike in Minimum Wage)

6月19日毎日新聞

政府は労使代表と構成する「成長力底上げ戦略推進円卓会議」に、これまで生活保護費を基準に設定してきた最低賃金を、今後5年間で高卒初任給の最低水準まで引き上げるよう提案する方針を固めた。07年の水準に当てはめると、全国平均の687円(1時間当たり)を755円に引き上げる必要がある。20日の円卓会議に提案するが、使用者側は経済状況を理由に難色を示す可能性がある。

最低賃金は、中央最低賃金審議会が目安を設定し、各地方の審議会が具体的な額を決める。円卓会議の議論はこの流れに大きな影響を与える。 円卓会議は、低所得者層の賃金改善などを議論する場として設置された。昨年末をめどに最低賃金の中長期的な引き上げ方針をとりまとめる予定だったが、労使の意見の隔たりが大きくまとまらなかった。



議論の読み方
まず最低賃金で雇用者の雇用は向上するのか?2つの議論がある。

ひとつは、雇用者の雇用状況は改善しない。理由は最低賃金の向上により、使用者が労働者の採用を見送る可能性がある。これは従来の経済学の見解。

もうひとつは、雇用者の雇用環境は改善する可能性がある。アメリカの経済学者David Card and Alan B. Kruegerの有名な研究であるが、地域独占などにより、最低賃金が労働者の雇用を減らさない可能性がある。

どちらを取るにせよ、最低賃金の引き上げが必ず雇用者の生活を改善するかどうかは定かでない。いいことだと歓迎できない。

My Opinion
A raise in Japan's minimum wage has been decided. Will it boost up employment? That's the question.

We have mainly two arguments about this matter.

(1) It reduces employment.
If minimum wage is up, the employers won't want to hire more employees. As a result, lower-wage employees can be unemployed.

(2) It doesn't reduce employment.
If minimum wage is up, the employers might increase the wage to hire more employees. As a result, lower-wage employees can be paid higher(according to David Card and Alan B. Krueger).

I am not sure if employment will be up or not by raising up minimum wage. Anyway, I wouldn't have to give a welcome to this policy change because it is not clear whether such a raise will raise employment.


(Reference)
(1) The Economics of Minimum Wage Legislation, George J. Stigler, The American Economic Review, Vol. 36, No. 3 (Jun., 1946), pp. 358-365

(2) Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania, David Card and Alan B. Krueger, The American Economic Review, Vol. 84, No. 4 (Sep., 1994), pp. 772-793

衆愚政治

6月18日23時0分配信 毎日新聞

宮崎県の東国原英夫知事は18日の県議会本会議の終了後、記者団に「体罰は愛のムチ。昔はげんこつで教えられたが、最近はできなくなっている。愛のムチ条例はできないか」と発言した。この日は一般質問があり、印象に残った質問を問われて、突然「愛のムチ条例」に言及した。

議会では、自民党議員が教育問題を取り上げた。東国原知事は「宮崎県で『愛のムチ条例』や『愛げんこつ条例』はできないか。愛という範囲で条例化すべきだ」と語った。


産経新聞
 橋下知事は記者会見で、「新人ではなく、40歳代くらいの職員を対象に自衛隊での研修を検討したい」とし、「府庁の事務職にどっぷり慣れ親しんだ職員に、あいさつ、姿勢から学んでほしい。僕も含めて」と述べた。実現できるかどうかは分からないとしながらも、同日午後に開かれる部長会議で提案したいという意向を示した。



雑感
やはり政策構想に欠けているのか。愛のムチ条例、これで子供への教育効果はあるのか?

自衛隊体験入隊、これで府職員の業務効率は向上するのか?

何のために、その政策を行うのか? 

政策を立案、検討、そして議会に提出、了承、そして施策へと膨大な時間と労力を要する。税金が使われるのである。

人気取り、目玉として、効果が定かでない政策に膨大な税金を投じるのは危険極まりない。政策構想に必要なのは、B/C、費用対効果の発想である。情緒的な発想ではない。

Wednesday, June 18, 2008

ミルウォーキの晴れ


晩飯

日本と同じ食事。サッポロ、やきそば。

シカゴにて(2)

どこかで見た光景。シカゴの風景。
It looks like somewhere in Japan. It's in Chicago.

中之島?
Nakanoshima?

天満橋
Tenmabashi?


福島?
Fukushima?

心斎橋?
Shinsaibashi?
堂島?
Dojima?

そう、なんとなく大阪の風景に似ている。そう感じるのは小生だけだろうか?
Chicago looks somewhat like Osaka in scenery, doesn't it?

シカゴにて







なんとなくシカゴ(Chicago, IL)にて

ミルウォーキの書斎


ミルウォーキの夕暮れ



ミルウォーキの6月







ミシガン湖の畔にて。

ミルウォーキ花屋敷






京阪神沿線の人にはお馴染みの雲雀丘花屋敷をもじって。

Tuesday, June 17, 2008

蟹工船、未来、「新しい考え」

2008年10月13日追記、修正

「蟹工船ブーム」

蟹工船が日本でちょっとしたブームらしい。日本の階層格差社会が喧伝されて久しいが、その煽りか?

小生、蟹工船は読んだことがない。今日資本主義社会の限界に直面している、と早急な結論を出す向きもあるが、蟹工船の時代といまはそもそも同じなのか?

日本は比較的豊かな国だと信じるし、ストリートチルドレンや貧民街と呼ばれる地域は存在しない。
(いわゆるアイリン地区(大阪西成区)は貧民街ではなく、歴史的に見て、日雇い労働者の溜まり場に過ぎない。これを貧民街と見ることもできようが、あの地域に貧しい家族や子供が住んでいるわけでは特にない。)

新しい時代
今は新しい時代に差し掛かっていることは確かだ。しかしそれは資本主義の限界とか新しい社会主義、共産主義の到来ではなく、資本主義社会が新しい時代に直面している、ということである。

大まかに見て、先進国は少子高齢化に直面し、低成長の中高齢者を支えるために増税の必要性に直面している。対して、発展途上国は人口の増加の勢いがとまらず、高成長の中都市と農村の経済格差は拡大、環境汚染が深刻化し、貧乏人と金持ちの格差は拡大の一途をたどっている。

いずれにせよ、経済成長の果実が経済社会の構成員に等しく分け与えられない(資源が若者から年寄りへ、労働者から金持ちへ、という具合に)という問題を抱えている。これは新しい課題ではなく、カール・マルクスが生きた時代からある古典的な問題である。

しかし、今の日本で生活が苦しいという実感は根強いが、こういうことをいう人たちは大概私より上の世代である。つまり明るい未来が約束されたかに見えた高度成長を知る「団塊の世代」か、それよりも少し後の世代である。そういう世代に人からすると、今は苦しいかもしれない。

私の世代は、就職氷河期だといわれ、不本意な仕事でも歯を食いしばって黙々と働くことが疎まれつつも、高く社会的に評価されるのではないかとひそかに期待している世代ではなかろうか。未来は掴み取るのではなく、寝て待て、という「大人しく現実志向の世代」。

現状や先入観、世間の常識に反論しない。ある意味、保守的で堅実で比較的質素な生活態度を志向する「若年寄の世代」。そう考えている。

ある大学教授の見を思い出す。「今の子はおとなしいので、指導がしやすい。」全学連世代を知る老教授は、皮肉を込めてなのか、われわれの世代をこう評する。企業の人事担当者も今の子は「大人しい」という。そうかもしれない。

未来がわからない
われわれの世代が比較的おとなしいと評される背景には、比較的未来が描きにくくなったことがあるかもしれない。しかしこれは、今に始まったことなのか。

イギリスの経済学者リカードの生きた時代、まさに工業資本主義の勃興期。機械工業が発達し、イギリスは「世界の工場」と評された。しかし一方で、機械の導入で仕事の機会が奪われたかに見えた工場労働者は自らの失業の原因を機械に求めた。機械打ちこわし、「ラダイト」(Luddite movement)である。

しかし、その後どうなったか。やがて労働者は新しい職に就き、前世代よりもよりよい時代を築いた。

ちょうどそのような時代に似ているのではないか。新しい仕事、新しい未来が過去の延長線上に見えない。不安におびえ、だからこそ既成の概念、制度、風習そして組織に依存せざるを得ない。

まさに、今の我々の世代の態度である。「大人しさ」の背景には「不透明な未来」があるのだ。

「新しい考え」
未来は見えない。だから不安である。それはむしろ自然だ。

不安を和らげるため、不安を乗り越えるため、そして、不安の先に見える近い将来を生き抜くための「新しい考え」が新しい時代には必要なのかもしれない。

私はその考えがどのようなものかはまったく見当がつかないが、たぶん意外に我々の身近にあるものかもしれないと感じている。たとえば、それは我々の歴史の中に、我々の先輩の中に埋もれているかもしれない。

蟹工船ブームは、まさに「新しい考え」が古い世代と遠い歴史の中にあるのではないかという大方の人々の実感を表しているかもしれない。一部の人が指摘するように、「それは現代なのだ!」と。

「新しい考え」から「新しい生活」へ
またこういった回顧的風潮こそが「現代」という時代の見通しの悪さ、新しい事態への不安を証憑しているのではなかろうかとも勘繰りたくなる。「新しい考え」が古い考えの中にあるというある種の説得はそういった見通しの悪さへの対処法だと喧伝されるが、結局は「新しい考え」はわれわれの生きる今の時代にしか存在しないのではないか。

今の時代と蟹工船の時代とは明らかに似て非なる世界だ。今のほうが物質的に恵まれている。結局我々の先人がその時代の考えを作ったように、「新しい時代」に生きる我々こそが「新しい考え」を作っていかねばならないと思うし、その営為を惜しんではならない。古い考えに固執してはならないし、古い考えから学ぶことは知的賞賛に値せずむしろ知的怠慢だ。

今はチャンスではないか。新しい考えの先に「新しい生活」が待っている。そう期待してもいいのではないか。理想的な生活を思い描くことで「新しい考え」が見えてこよう。そしてその「新しい考え」を作るのは我々の世代的課題なのである。

Corporate Income Tax (3): Dynamic Analysis

I would have to say that one of the main purposes of this blog is to let you have an interest in modern economics. Today I try to accomplish it.

Last time I talked about the static analysis of the corporate income tax by using the simple Keynesian cross.

This time I would like to explain the the dynamic analysis of the corporate income tax by using the simple neoclassical growth model(or the Ramsey model).

The model is simple. There's only one consumer with a perfect foresight in a perfect competitive market. To make this model simple, it is assumed to be an infinite horizon problem . Moreover, no externality, no uncertainty and no heterogeneity.

The consumer just aims to maximize his or her lifetime instantaneous utility that is assumed to be a strong increasing and strong concave function subject to the resource constraint.

The objective is,

max U(C(0))+βU(C(1))+β^2U(C(2))+....+β^tU(C(t))
+
β^(t+1)U(C(t+1))+.
.....,

where C(t) is his or her consumption level and β is a discount factor with 0<β<1.

The resource constraint is,

s.t. K(t+1)-K(t)=(1-y)(F+rK(t))-(1+c)C(t), K(0)=given


where K(t) is the capital stock, F, the income level, y, the (corporate) income tax rate, r, the real interest rate and c, the consumption tax rate.


To solve this problem, there are mainly three ways to do it, the Lagrangian method, the maximum principle (MP) and the dynamic programming (DP). Which way to choose relies on your preference, but these three algorithms definitely lead us to get the same solution.

The solution is called the Euler equation. By looking over it, we can see what policy affects what variable and the optimal path of the variable and some important implications, which are somewhat different from what we got from the static analysis of the corporate income tax.


(1)The Lagrangian function is:

L(C(t), K(t), λ(t))

= U(C(0))+
βU(C(1))+β^2U(C(2))+....+β^(t-1)U(C(t-1)) +....

-λ(0)(
K(1)-K(0)-(1-y)(F+rK(0))+(1+c)C(0))

-λ(1)(
K(2)-K(1)-(1-y)(F+rK(1))+(1+c)C(1))+....

-λ(t-1)(
K(t)-K(t-1)-(1-y)(F+rK(t-1))+(1+c)C(t-1))+....

This model is a discrete time version. So if we want to get the Hamiltonian dynamics for this problem, we should take the limitation to change the discrete to the continuous time version of this model.


(2)The current valued Hamiltonian function is:

H(C(t), K(t), λ(t))=
U(C(t))+λ(t)(K(t)+(1-y)(F+rK(t))-(1+c)C(t))

(3)The Bellman equation is:

V(K(t))=max{ U(C(t))+βV(K(t+1))

s.t. K(t+1)-K(t)=(1-y)(F+rK(t))-(1+c)C(t), K(0)=given }

We solve for the function, and C(t)=P(K(t)) is called the "policy function".

Regarding (3), it is assumed that there's the value function that satisfies the above Bellman equation for this problem(That is, we assume that the Blackwell's theorem holds in this problem).

The Euler equation is,

U'(C(t))/
U'(C(t+1)) = β{(1-y)r+1}

In addition to the transversality condition (TVC), we can get the optimal path of the consumption growth. The Euler equation is the ratio of the marginal utilities of the consumption between the period t and period t+1.

Looking at this equation,

(The marginal utility of t-period consumption) = U'(C(t)),

(The present value of the marginal utility of t+1-period consumption)

= U'(C(t+1))
β{(1-y)r+1}

in our optimal solution we can see the equality between the marginal utility of t-period consumption and the present value of that of t+1-period consumption. This is the optimality condition that we've wanted to get for this problem.

We can see that only the rate of the corporate income tax affects the consumption growth(if we assume that the utility function is a logarithmic form, U(C(t))=lnC(t) ). The tax rate influences the efficiency of the economy! That is, the higher the income tax rate, the lower the consumption growth in the case of the logarithmic utility.

From the perspective of the dynamic analysis, the corporate income tax definitely affects the economy(more accurately, economic efficiency), whereas it doesn't in our static analysis. That's what I want to put emphasis on here.


06/17/08, Postscript,

Some people say that cutting the tax rate of consumption would increase the consumption or its growth rate. However, according to our analysis, cutting the consumption tax would neither increase nor decrease the consumption growth.

It seems peculiar, but it's a well-known result for such a problem. Why not? It's easy. The consumer in this problem can expect it accurately if the government increases the consumption tax. That's why he or she will change the optimal path of his or her consumption beforehand and thus there's no difference.

果物あれこれ

まずは、西瓜。価格は、400円ぐらい。

次はこれ。穴の中がくさ~い。

少し甘い。
パパイヤ。価格は600円ぐらい。

いずれも日本にない果物。また日本で見かけない果物を紹介しよう。

Tuesday, June 10, 2008

No Tomato

Today I had a hamburger at Burger King but there's no tomato. Why?

Friday, June 06, 2008

Income Tax (2): Static Analysis

02/04/2014 Revised

Recall the Keynesian cross, where there's one consumer and no producer.

The equilibrium of the aggregate economy: Y (aggregate supply) = E (aggregate demand) .....(1)

where Y= (constant).

The aggregate demand is: E = C (consumption) + I (investment) .....(2)

where I = (constant) .

The aggregate consumption is assumed to be the Keynesian version: C = a(Y-T) + c .....(3)

where a and c are both constant.
a is greater than 0 and less than 1. c is greater than 0. T is a tax.

The income tax t1: T=t1Y, C=a(1-t1)Y + c, E=Y .....(4)

The consumption tax t2 : T=0, E=(1+t2)Y.....(5)

The size of the effect of each tax on the demand:

income tax t1: 1/(1-a(1-t1)) .....(6)

consumption tax t2: 1/(1-a+t2)  .....(7)

If t1=t2, then 1/(1-a(1-t1)) is greater than 1/(1-a+t2). Then, the effect of income tax is greater than that of consumption tax.

Corporate Income Tax (1): Tax Incidence

When I was an undergraduate student of economics, I found that it was a very interesting column in Mankiw's text and I began to think about what the most efficient tax is like.

Tax policy, as Prof. Mankiw says, is not only about economics but also about political economy. When we discuss and think about how well the tax policy should be conducted, we have to keep in mind that the burden of the tax ultimately falls on people.


Mankiw: Who Pays the Corporate Income Tax?

....People pay all taxes,...the owners, customers, or workers of the corporation.

Suppose that the U.S. government decides to raise the tax on the income earned by car companies.

(1) hurts the owners of the car companies

⇒ (2) receive less profit

⇒ (3) invest less in building new car factories & more in other factories

⇒ (4) the supply of cars and the demand for autoworkers decline

⇒ (5) the price of cars to rise and the wages of autoworkers to fall

⇒ (6) autoworkers get poor

This case is about the tax falling on car companies, but if we assumed high tax on the income earned by all the companies in the US, the effect of that tax would be large.

Wednesday, June 04, 2008

Greg Mankiw's Blog: Really Good Idea?!

In Japan, my home country, an economic policy aiming to cut the corporate income tax is popular among business society, policymakers and economists.

Business society like low corporate income tax because they don't have to pay high tax. Policymakers, and worse, economists also like it because they can get more political and financial support from the business society.

However, I don't understand why this kind of policy is so popular. Greg Mankiw, my favorite economist of Harvard, posts a readable article in the NY times.

He says, "Don’t laugh. I’m serious." It seems worth reading. Shall we listen to him? Why does he support a cut in the corporate income tax?


There are three main points:

(1) The corporate income tax promotes long-run growth in American living standards.


The idea is so simple: a cut in the corporate tax would boost after-tax profits and stock prices, which results in a stronger stock market and more capital investment. More investment would lead to greater productivity, which leads to higher wages for workers and lower prices for customers.

This kind of idea is so-called "supply-side economics": if the tax on company decreased, many companies would increase their production and employment, and thus profit and income. Increased income should go to workers, that is, consumers and they should buy more consumer goods and become happier. The tax cut strengthens not only the supply side(production), but also the demand side of the economy(purchase).

It sounds reasonable, but do increased profit and income really go to consumers? That's the question.

It may sound Marxian, but it doesn't seem to me that increased profit goes to workers and consumers. Increase profit may go to stockholders, not to workers. Stockholders are generally rich and may have relatively lower propensity to consume than that of workers(That's why rich people hold stocks).

In addition, more people are not stockholders but workers. Thus, less workers spend much and more stockholders spend less. As a result, low corporate income tax doesn't boost up well the demand of the economy.

Mankiw raises this problem in his introductory textbook of economics as an example of Kennedy's tax cut in 1963. This tax cut was not the cut of the corporate income tax. Moreover, it was so Keynesian and aiming to stimulate the demand side.

However, it also raised the supply side of the economy. The production was up.

In the 1960s, the America seemed to have really a bright future (people thought they could become happier than yesterday) even though there were some serious political risks like the Cuban missile crisis and the Vietnam War.

If people (consumers) thought they could become happier than yesterday, they would purchase more in the store and would get higher living standards. But if the reverse happened, what would happen? They should save more of their income and cut their living expense just as a safety precaution.

Good expectation makes people behave like a bull, but bad expectation doesn't. Mankiw doesn't seem to think about a role of people's expectation on the future.


(2) The ultimate payers of the corporate tax are the individuals who have some stake in the company on which the tax is levied.


Mankiw raises some nice researches: William C. Randolph of the Congressional Budget Office concludes that domestic labor bears slightly more than 70 percent of the burden of the corporate tax.

Wiji Arulampalam, Michael P. Devereux and Giorgia Maffini conclude that a substantial part of the corporation income tax is passed on to the labor force in the form of lower wages, adding that in the long-run a $1increase in the tax bill tends to reduce real wages at the median by 92 cents.

These researches are persuasive and I agree on this point.

Mankiw also writes about this point, raising an example of the tax on rich people: high tax on luxury goods seems a good way to tax rich people more heavily, but in reality the reverse would happen: it taxes not rich people.

More precisely, high tax on luxury goods is imposed on producers of the luxury goods and, maybe, the workers of the producers. The workers at the company which produces luxury goods are generally not rich.

The luxury good tax sounds nice for the sake of equity, but it lies heavy on not rich people.


(3) The distortions that the corporate income tax induces are large compared with the revenues that the tax generates.


This point seems more important than the above 2 points. Tax distorts incentives. Tax affects the people's behavior and changes the economy to a Pareto-inferior equilibrium (brings the deadweight loss).

Mankiw points out, "compared with other ways of funding the government, the corporate tax is particularly hard on economic growth." Reducing these distortions would lead to better-paying jobs.

I also agree on this point but we have to keep in mind that tax affects the people's behavior.

Mankiw gives an example of Mr. Randolph’s analysis, the role of international capital mobility: low corporate income tax lures foreign investors.

Savings search the highest returns in the world capital market. The domestic capital owners can escape most of the corporate income tax burden when capital is reallocated abroad in response to the tax.

Following this line of the argument, if the corporate tax decreased, more capital would come in from abroad and thus more investment and more production would be realized. It sounds reasonable, but is it true?

As you know, a famous research conducted by C. Horioka and M. Feldstein shows high correlation between domestic investment and savings, which means that capital doesn't move more freely than we imagine.

Investors in one country do not need the funds from domestic savers and can borrow from international markets at world rates. By the same token, savers can lend to foreign investor the entirety of the domestic savings. So low correlation between them might be observed, but in fact it isn't.

This result is seen as evidence of low capital mobility and is so-called Horioka-Feldstein puzzle.

Corporate income tax distorts people's incentives and thus it's very serious in terms of economic welfare. However, the high gasoline tax as Mankiw proposes also distorts incentives.

Low corporate tax and high gas tax look a very nice combination, but what does this combination of tax bring?

High gas tax reduces gas emission and traffic jam, which leads to better living environment. But it taxes drivers, not gasoline itself?

I think that a Pigouvian tax is a good idea but I would like to keep in mind that this tax would also hurt drivers' (people's) economic welfare and convenience as well as the corporate income tax would do.


(References)
(1) Feldstein, Martin & Horioka, Charles (1980), “Domestic Saving and International Capital Flows”, Economic Journal 90: 314-329

(2) The Pigou Club Manifesto, Greg Mankiw's Blog, Friday, October 20, 2006.

(3) Corporate Tax Rates, Greg Mankiw's Blog, Wednesday, May 03, 2006.

Greg Mankiw's Blog: Cut the Corporate Income Tax

Monday, June 02, 2008

Go to Potsdam

I am going to Potsdam, Germany at the end of June. This is one of the exchange programs offered by my university. This is a one-month stay at Potsdam. It's very short, but may be a good and precious chance to go and see another country, so I decided to go there. It should be a good memory for me. (Moreover, the cost is paid by the university, not me.)

By the way, many Japanese and other foreign students may think that studying abroad is going to the US. In fact so do I and that's why I came here. Potsdam may also be a good place to study something.

Potsdam is a historically and maybe mentally important place for Japanese people, though. It is a famous place in Japan. Near the end of the World War 2, the Allied Forces discussed how to ask Japan to surrender unconditionally at this place.

It's a long time ago, but many people all over the world are still suffering from such memories of the war. I cannot imagine how severe their hardships are, but I can touch on their feeling if I try to do.

Anyway, this is not the trip to learn the history of the World War 2, but to learn the monetary policy and system in the EU. I seize on this chance to learn about these area.