The Business-Stealing Effect is Wrong

The Business-Stealing Effect is Wrong.hwp

 

JEL Classification: O33, O40, D60

Keywords: business stealing effect, pecuniary externality, innovation, endogenous growth, hazard rate

Abstract

Now it is believed that if the innovation is drastic and so it makes the existing technology useless, then there is the possibility of more R&D than socially optimum, for researchers do not internalize the destruction of existing rents created by their innovations. But even the social planner does not need to internalize the loss to the previous monopolist(leader) caused by an innovation. It was considered when the leader did R&D. The leader's present profit was not considered as eternal from its birth. All the participants in the drastic innovation know that their profit of winning can obsolesce in the near future. In general, the pecuniary externality cannot cause inefficiency if we exclude the second best approach. The business-stealing effect is the pecuniary externality. It is the shift of demand from old technology to new technology in the market. So it cannot cause inefficiency. The business stealing effect is just nonsense. There is no object of stealing after the expected duration of the technology. Their conclusion is only a math error.

1. Introduction

Now the R&D approach of Grossman and Helpman(1991), Aghion and Howitt(1992) is accepted as the state-of-the-art endogenous growth theory. But their papers are based on wrong calculation.

They insist that if the innovation is drastic and so it makes the existing technology useless, then there is the possibility of more R&D than socially optimum, for researchers do not internalize the destruction of existing rents created by their innovations.

Grossman and Helpman(1991), Aghion and Howitt(1992), Barro and Sala-i-martin(1995) make models in which the leader(incumbent) does no R&D. Under this assumption they try to prove the possibility of excessive R&D. They interpret this excessive R&D stems from the business-stealing effect that the introduction of a superior technology typically makes existing technologies less attractive, and therefore harms the owners of those technologies.

D. Romer(1996, p. 114.) insists that the business-stealing effect can cause inefficiency in the monopolistic situation even if it is is the pecuniary externality. Barro and Sala-i-martin(1995, p. 261.) insist that if the leader is endowed with property rights over her monopoly profit, then the business-stealing is prohibited and the possibility of excessive R&D disappears.

But all these assertions are wrong. The business-stealing effect is the pecuniary externality and it cannot cause inefficiency.

2.The Business-Stealing Effect has Nothing to do with Efficiency

Even if the business-stealing is prohibited by compensating the incumbent, as Barro and Sala-i-martin insist, there is no change in R&D investment in Grossman and Helpman(1991)'s, Aghion and Howitt(1992)'s, Barro and Sala-i-martin(1995)'s models [Figure 1]. The decreased incentive of the challengers is offset by the increased incentive of the protected leader. If there is no compensation, then the leader thinks her profit will be obsolete in the near future. But if there is compensation, the leader's profit becomes eternal and her R&D incentive increases greatly. The sum of profit that is endowed to the protected leader and her successor does not change by compensation. So, if we assume the distribution of profit does not change the aggregate R&D, there is the same amount of R&D after compensation.

   No Compensation                          With Compensation

		3rd firm					3rd firm
	2nd firm					2nd firm
1st firm					1st firm

Figure 1. The profit of no compensation and after compensation.

Even if the challenger is the social planner, the challenger does not need to internalize the loss to the previous monopolist(leader) caused by an innovation. It was considered when the leader did R&D. The leader's present profit was not considered as eternal from its birth. All the participants in the drastic innovation know that their profit of winning can obsolesce in the near future. Even when the leader loses and business-stealing happens, it cannot cause excessive R&D since it was expected and the leader's past investment already had reflected that possibility. In fact, it makes no difference to the profit from the present technology whether the leader wins or the challenger wins.

If the new innovation comes earlier than the leader expected, the leader's past R&D investment becomes failure and excessive R&D, for the leader cannot have as much profit as expected. But it is about ex post. If the expectation about the duration of the innovation is correct, then there is no possibility of excessive R&D. If there is an expectation about the duration of the innovation, we cannot say the possibility of the excessive R&D ex ante.

In general, the pecuniary externality cannot cause inefficiency. D. Romer(1996, p. 114.) insists that when there are departures from perfect competition, pecuniary externalities can cause inefficiency. This is wrong. The cause of inefficiency is not the pecuniary externalities but the departures from perfect competition. If the departures from perfect competition disappear, inefficiency disappears regardless of the pecuniary externalities. But even if the pecuniary externalities disappear, there can be inefficiency when there are the departures from perfect competition. If we considered the second best approach, his assertion might have meaning. If there is market failure in a certain market and we cannot correct it, then we should calculate all the consumer surplus and producer surplus for the second best solution.

But Grossman and Helpman(1991), Aghion and Howitt(1992), Barro and Sala-i-martin(1995) do not use the second best approach in deducing socially optimal R&D. So it is impossible that the business-stealing cause inefficiency in their models. The possibility of excessive R&D presented in their models stems from wrong calculation.

3. Wrong Calculation

1) Aghion and Howitt(1992) and Grossman and Helpman(1991)

① Aghion and Howitt(1992)

They interpret (mean) of Poisson distribution(in their model ) as the probability of innovation success. This is wrong. Their equation (2.9) is wrong. So their market level of research is wrong and the market growth rate is wrong.

They make another mistake. Equation (4.1) and (4.3) is wrong. They apply as the expected utility of t innovations up to time . This is wrong. is the utility of after (t)th innovation. The utility is not before (t)th innovation. is only the probability of t innovations up to time . It does not say when and with what probability 1st, 2nd, ․․․(t-1)th, (t)th innovation happen. So their socially optimal level of research is wrong and the socially optimal growth rate is wrong.

② Grossman and Helpman(1991)

They make exactly the same mistakes as Aghion and Howitt(1992).

Their equation (9) is wrong. They interpret (mean) of Poisson distribution(in their model) as the probability of innovation success. So their market level of research is wrong and the market growth rate is wrong.

Grossman and Helpman shirks the second problem by substituting their equation into their equation(2). Their equation(5) is all expenditure is spent to the state-of-the-art quality product. But substituting equation(5) into equation (2) is possible only to the case of one innovation. If there is more than one innovation we cannot substitute equation(5) into equation(2). If we do, the contradiction that firms invest even though there is no demand to the intermediate innovations happens. If we consider that any innovation has its demand until the next innovation comes, their mistake becomes clear. [Segerstrom(1991. p. 820.) makes the same mistake as Grossman and Helpman. His equation (29) is wrong.] In result their equation (12) is wrong. So their socially optimal level of research is wrong and the socially optimal growth rate is wrong.

③ How does the possibility of excessive R&D happen in their models?

Their calculation gives a great rise to the market level of research. In their models the R&D investment increases . When increases the probability of innovation success increases by the same ratio since is equal to the probability of success. But it is false. When is 0.1 the probability of one innovation success in a unit time is 0.09. When is 0.2 the probability of one innovation success in a unit time is 0.163. When is 1 the probability of one innovation success in a unit time is 0.368. When is 2 the probability of one innovation success in a unit time is 0.271.

Why do we use Poisson distribution? Because under Poisson distribution the probability of success cannot be greater than 1 how further the time goes. But in their calculation the probability can go beyond 1 since the R&D investment increases and their is the probability. In their models the marginal benefit of R&D can be exaggerated since the probability of success increases by the same ratio as . This is the source of the possibility of excessive market R&D.

In fact their socially optimum R&D is exaggerated too. In the case of multiple innovations, they consider the benefit that is enjoyed after the last innovation as the benefit of the multiple innovations.

2) Barro and Sala-i-martin, 1995. p. 249. and p. 260.

They interpret (mean) of Poisson distribution(in their model ) as the probability of innovation success within a unit period. Their equation (7.20) and (7.46) are wrong. So their market growth rate and social planner's growth rate are wrong.

They insist that there is the possibility of excessive R&D since the challenger has no need to compensate the leader. But compensation cannot change the incentive of R&D. [Figure 1]

4. Is hazard rate a probability?

Let's assume Poisson distribution the mean of which is λ. Then the probability of waiting until time t (no innovation until time t) is

   1 - F(t) = e^-λt.

The probability density function of innovation success time is

   f(t) = λe^-λt.

So hazard rate is

   f(t)/(1-F(t)) = λ.

Now can we use λ as the constant, perpetual, instantaneous probability? No, we cannot. The economists who use λ as the constant, perpetual, instantaneous probability are wrong.

1) Probability Density Function?

What is their probability density function? What is the time interval they consider? We need a time interval to get the probability from a probability density function. In the continuous model, without the time interval the probability is always zero. If their probability density function really were, then could we get 1 by integrating their probability density function?

They say the probability density function is constant λ. Then time is limited to 1/λ. Is it plausible?

2) What does f(t)/(1-F(t)) mean?

λ is hazard rate. Hazard rate is not a probability. What is hazard rate? Hazard rate is a decrease rate of the survival function. (Greene, 1997. p. 987., Lawless, 1982. p. 9., Cox and Oakes, 1984. p. 14.)

λ(t) =

If we assume Poisson distribution, then the probability density function of innovation success time is exponential distribution f(t) = λe^-λt. The survival function, the probability of waiting until time t (no innovation until time t), is 1-F(t)=e^-λt. And hazard rate is constant λ.

What does a decrease rate of the survival function mean? As time goes, the probability of innovation success increases. The probability of the present technology's survival decreases. Hazard rate indicates how fast it decreases as time goes. A growth rate of economy indicates how fast economy grows. Anyone does not insist that a growth rate is a probability. Hazard rate indicates how fast a certain probability decreases. Hazard rate in itself is not a probability but a rate.

3) The instantaneous probability is not f(t)/(1-F(t)) but f(t)

Hazard rate is f(t)/(1-F(t)). It is not a probability but a CONDITIONAL probability. Here 1-F(t) is condition. And the condition changes continually as time goes. Conditional probability density functions are totally different if their conditions are different. We cannot make a new distribution by selecting some portions from different distributions. It is nonsense.

λ needs the condition that the innovation is not ready until t. If we want to use λ as "the constant, perpetual, instantaneous probability," we should always assume that the innovations is not ready until time t. This has a contradiction in itself. Let's think about two time instant, t=2 and t=3. They say the instantaneous probability at t=2 is λ. Also they say the instantaneous probability at time t=3 is λ. At time t=3, they need the condition 1-F(t). It means there is no innovation until time t=3. Then they should assume the instantaneous probability at time t=2 is 0. How can they solve this contradiction? The instantaneous probability at time t is f(t). Why do they ignore f(t)?

4) f(t)=λ*S(t)

λ =

f(t)=λ*S(t)=λ*(1-F(t))

These equations will clear confusion. f(t) is the right probability. λ, hazard rate, is a decrease rate of the survival function. S(t), the survival function, is  the probability of waiting until time t (no innovation until time t). So f(t), the instantaneous probability, is S(t) multiplied by λ. f(t) is the instantaneous decrease of S(t).

Kamien and Schwartz(1972. pp. 46-47.), Loury(1979. p. 398.), Lee and Wilde(1980. p. 431.), Dasgupta and Stiglitz(1980. p. 15.), Mortensen(1982. p. 969.), Reinganum(1982. p. 674.), Reinganum(1985. p. 85.), Dixit(1988. p. 319.) and most other economists use λ*S(t) (hazard rate multiplied by the survival function) as the instantaneous probability since this is right.

5. conclusion

They confuse a rate (hazard rate) with a probability. In Poisson distribution, lamda is totally different from a probability. When lamda is 0.7 the probability of one innovation per unit time is 0.347 and the probability of more than one innovation per unit time is 0.156.

And their second mistake about socially optimum growth rate is based on lack of understanding about Poisson distribution.

Appendix

1. Someone says their calculation is based on Poisson postulates

He cites Lindgren(1968. p. 162.)

Poisson Postulates

1. Events defined according to the numbers of failures in nonoverlapping intervals of time are independent.

2. The probability structure of the process is time invariant.

3. The probability of exactly one failure in a small interval of time is APPROXIMATELY proportional to the size of the interval.

4. The probability of n failure in a small interval is NEGLIGIBLE in comparison with the probability of one failure in that interval.

He asserts their calculation is based on 3. 4.

But his assertion is approximately right only on a infinitely small interval. But the model should assume the real world. The real world is not a infinitely small interval. The real world is the sum of the infinite number of the infinitely small intervals. If the earth were to end in a infinitely small interval his conclusion would be right approximately.

We should consider "approximately" and "negligible." The real world is the sum of the infinite number of the infinitely small intervals. The sum of the infinite number of "approximately" and "negligible" can not be negligible. We can not apply these necessary conditions (3. and 4.) to the model that does not premise a infinitely small interval. It is approximately right only to a infinitely small interval.

2. About the assertion that their model is continuous and so they could be right.

Someone insists that their calculation is right since their model is continuous. If firms consider infinitely small time interval, his assertion could be right.

What is the continuous model? "Continuous" means that the model uses flow(continuous) variables, i.e., the flows of profit and cost and the continuous probability density function. "Continuous" is not equal to the infinitely small time interval. In the continuous model the calculation should always be right regardless of time intervals.

In their models, do the stupid firms consider only infinitely small intervals? So their calculation could be right? No, they assume rational firms.

And these assertions cannot say anything about the second problem(socially optimal R&D)

3. Math error of Barro and Sala-i-martin(1995)

Their equation (7.17) in page 248 is totally wrong. At page 247 they say P(jkj) as the probability  per UNIT time of a successful innovation. P(jkj) needs a time INTERVAL(a PERIOD). But they use P(jkj) with an instantaneous value, dG/dτ. They confuse a value of probability density function with a probability. Probability is an integration value of probability density function. Probability is totally different from a value of probability density function. Their equation (7.17) is right if we replace P(jkj) with lambda.

References 

Aghion, P. and Howitt, P. 1992. "A Model of Growth through Creative Destruction," Econometrica, 60, 323-351.

Aghion, P. and Howitt, P. 1998. Endogenous Growth Theory, Cambridge, Mass.: MIT press.

Barro, R. J. and Sala-i-martin, X. 1995. Economic Growth, New York McGraw-Hill.

Cox, D. R. and Oakes, D. 1984. Analysis of Survival Data, London: Chapman and Hall.

Dasgupta, P. S. and Stiglitz, J. E. 1980. "Uncertainty, Industrial Structure, and the Speed of R&D," Bell Journal of Economics, 11, 1-28.

Dixit, A. 1988. "A General Model of R&D Competition and Policy," Rand Journal of Economics, 19, 317-326.

Greene, W. H. 1997. Econometric Analysis(3rd Edition), London: Prentice-Hall.

Grossman, G. M. and Helpman. E. 1991. "Quality Ladders in the Theory of Growth," Review of Economic Studies, 58, 43-61.

Kamien, Morton I.; Schwartz, Nancy L. 1972. "Timing of Innovations Under   Rivalry," Econometrica;  40, 43-60.

Lawless, J. F. 1982. Statistical Models and Methods for Lifetime Data, New York: John Wiley & Sons.

Lee, T. and Wilde, L.L. 1980. "Market Structure and Innovation: A Reformulation," Quarterly Journal of Economics, 94, 429-436.

Lindgren, B. 1968. Statistical Theory (2rd Edition), New York: Macmillan.

Loury, G. 1979. "Market Structure and Innovation," Quarterly Journal of   Economics, 93, 395-410.

Mortensen, D. T. 1982. "Property Rights and Efficiency in Mating, Racing, and Related Games," American Economic Review, 72, 968-979.

Reinganum, J. F. 1982. "A Dynamic Game of R&D: Patent Protection and Competitive Behavior," Econometrica, 50, 671-688.

Reinganum, J. F. 1985. "Innovation and Industry Evolution," Quarterly    Journal of Economics;  100, 81-99.

Romer, D. 1996. Advanced Macroeconomics, New York: McGraw-Hill.

Segerstrom, P. S. 1991. "Innovation, Imitation, and Economic Growth," Journal of Political Economy, 99, 807-827.

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Subject:              "The Business Stealing Effect is Wrong"

        Date:              Tue, 2 Jun 1998 09:42:16 EDT

       From:              "Gene Grossman" <grossman@wws.princeton.edu>

 Organization:             WWS

         To:             chose@ucs.orst.edu

         CC:              Helpman@ccsg.TAU.AC.IL

Dear Mr. Cho,

I have received your comment on my paper with Elhanan Helpman (and

others).  Your comment is incorrect.

With a poisson arrival process, the probability of a success in a

small interval of time of length dt is lambda*dt; i.e., it is

proportional to lambda.  The probability of two successes in this

interval is of order  (dt)^2, and so can be ignored.  Thus, the

situation about which you worry -- that two innovations happen in the

same "period" -- happens with probability zero.  In a continuous time

model, the periods are too short for this.

Helpman and I assume that all spending goes to the state-of-the-art

product, as you note.  Since two innovations cannot happen at the

same instant in time (except with zero probability), there is always

a single industry leader.  This leader earns monopoly profits until

the next innovation, which may come very soon after, or after a long

time.  In any event, the investors are well aware that their period

of leadership may be short.

I also found the tone of your comment to be offensive.

Sincerely,

Gene Grossman

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Subject:             Re: "The Business Stealing Effect is Wrong"

       Date:             Sun, 27 Sep 1998 11:08:48 -0700

      From:             cho <chose@ucs.orst.edu>

        To:             Gene Grossman <grossman@wws.princeton.edu>

        CC:            Helpman@ccsg.TAU.AC.IL

 References:             1

Dear Professor Grossman

My note was rejected by AER and JPE without any proper reason. They do not

consider my note seriously. only you considered my note seriously. Thank

you very much. But I am afraid that you have misunderstanding in Poisson

distribution and another math error.

1. You said

************

With a poisson arrival process, the probability of a success in a

small interval of time of length dt is lambda*dt; i.e., it is

proportional to lambda.

****************

"lambda*dt" is not probability. It is the mean of the success times.

2. You said

****************

The probability of two successes in this

interval is of order  (dt)^2, and so can be ignored.  Thus, the

situation about which you worry -- that two innovations happen in the

same "period" -- happens with probability zero.  In a continuous time

model, the periods are too short for this.

**********************

Let me give a simple example. When lambda is 0.7 (In your model lambda can

be any value. It can be more than one) the probability of one innovation

is 0.347 and the probability of more than one innovations is 0.156. How

small dt(time period) may be this proportion(0.347 : 0.156) does not

change.

lambda is not probability. lambda is the mean of Poisson distribution. It

is the expected times of occurrence. lambda*dt cannot be probability.

lambda*dt is the expected times of innovation during dt.

"The probability of two successes in this interval is of order  (dt)^2"

-- This is completely wrong. I wonder how you, one of the greatest

economist, get to think like this. Where is it written? Which statistics

textbook?

3. You said

*************

Helpman and I assume that all spending goes to the state-of-the-art

product, as you note.  Since two innovations cannot happen at the

same instant in time (except with zero probability), there is always

a single industry leader.  This leader earns monopoly profits until

the next innovation, which may come very soon after, or after a long

time.

**************************

It is quite right, as you say, that two innovations cannot happen at the

same instant and all spending goes to the state-of-the-art product. But

any innovation has its demand until the next innovation comes. Therefore

when we solve for socially optimal growth rate we cannot substitute your

equation (5) into equation (2). If we do, then we become to assume that

intermediate innovations cannot have any demand.

By substituting your equation (5) into equation (2) you separate 'q' and

apply Poisson distribution only to 'q.' But we should apply Poisson

distribution also to 'd' and 'p.' They change with 'q' at every

innovation.

Substituting equation(5) into equation (2) is possible only to the case of

one innovation. If there is more than one innovation we cannot substitute

equation(5) into equation(2). If we do, the contradiction that firms

invest even though there is no demand to the intermediate innovations

happens. If we consider that any innovation has its demand until the next

innovation comes, your mistake becomes clear. [Segerstrom(1991. p. 820.)

makes the same mistake as you. His equation (29) is wrong.]

**Segerstrom, P. S. 1991. "Innovation, Imitation, and Economic Growth,"

Journal of Political Economy, 99, 807-827.

I would be very pleased if you reply to this letter.

Thank you very much again.

With best regards,

Seonghun Cho

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Subject:              Re: "The Business Stealing Effect is Wrong"

        Date:              Mon, 28 Sep 1998 08:54:04 EDT

       From:              "Gene Grossman" <grossman@wws.princeton.edu>

 Organization:             WWS

         To:             cho <chose@ucs.orst.edu>

B. Lindgren, Statistical Theory, 2nd edition, Macmillan Publishing

Company, 1968, pp. 162-165.

A. Mood, F. Graybill, and D. Boes, Introduction to the Theory of

Statistics, 3rd edition, McGraw Hill, p.95.

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Subject:             Re: "The Business Stealing Effect is Wrong"

       Date:             Mon, 28 Sep 1998 11:41:17 -0700

      From:             cho <chose@ucs.orst.edu>

        To:             Gene Grossman <grossman@wws.princeton.edu>

        CC:            Helpman@ccsg.TAU.AC.IL

 References:             1

Dear Professor Grossman

Thank you very much for your reply.

Probably I understand the cause of your misunderstanding now.

Your calculation is based on

*************

B. Lindgren, Statistical Theory, 2nd edition, Macmillan Publishing

Company, 1968,

p. 162.

3. The probability of exactly one failure in a small interval of time is

APPROXIMATELY proportional to the size of the interval.

4. The probability of n failure in a small interval is NEGLIGIBLE in

comparison with the probability of one failure in that interval.

***********************

This is right only on the infinitely small interval. But the model should

assume the real world. The real world is not the infinitely small

interval. The real world is the sum of the infinite number of the

infinitely small interval.

You should consider "approximately" and "negligible." Your calculation is

wrong to the real world. Your conclusion is right only to the infinitely

small interval. The sum of the infinite number of "approximately" and

"negligible" can not be negligible.

If the earth were to end in a infinitely small interval your conclusion

would be right.

Do you agree to

1. Your conclusion is based on "The probability of exactly one failure in

a small interval of time is APPROXIMATELY proportional to the size of the

interval. The probability of n failure in a small interval is NEGLIGIBLE

in comparison with the probability of one failure in that interval."

2. The real world is not the infinitely small interval. The real world is

the sum of the infinite number of the infinitely small interval.

I would be very pleased if you answer my question.

Thank you very much again for your kind reply.

With best regards,

Seonghun Cho

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Subject:             About Poisson Distribution

       Date:             Tue, 29 Sep 1998 08:10:16 -0700

      From:             cho <chose@ucs.orst.edu>

        To:             Gene Grossman <grossman@wws.princeton.edu>

        CC:            Helpman@ccsg.TAU.AC.IL

 References:             1

Dear Professor Grossman

You said "In a continuous time model, the periods are too short for

this(more than 1 innovation)."

It is wrong. Continuous time does not mean short interval. Poisson

distribution premises continuous time.

**********

3. The probability of exactly one failure in a small interval of time is

APPROXIMATELY proportional to the size of the interval.

4. The probability of n failure in a small interval is NEGLIGIBLE in

comparison with the probability of one failure in that interval.

**************

These are the necessary conditions for a distribution to be Poisson

distribution. We should not use these in calculating Poisson distribution.

It is right only to very small interval.

If continuous time means short interval, your equation 12 is wrong. To

deduce equation 12 you consider m improvements.

I would be very pleased if you answer this letter.

With best regards, Seonghun Cho

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

Subject:             Re: "The Business Stealing Effect is Wrong"

       Date:             Sat, 03 Oct 1998 15:56:11 -0700

      From:             cho <chose@ucs.orst.edu>

        To:             Gene Grossman <grossman@wws.princeton.edu>

        CC:            Helpman@ccsg.TAU.AC.IL

 References:             1

Dear Professor Grossman

I think you have enough time to think about my letter. Would you reply as

soon as possible.

I attach another section to my note.

**************************

4. The History of Confusion

Grossman and Helpman(1991. p. 47.) say their calculation mimics the models

of Lee and Wilde(1980). Lee and Wilde(1980) say their calculation mimics

the models of Loury(1979). Loury(1979. p. 398.) says.

Thus, by making an investment valued presently at x, the firm "produce"

the constant, perpetual, instantaneous probability h(x) that the

innovation will be ready for the market at any subsequent moment. That is,

h(x)dt is the constant probability that if the innovation is not ready at

time t, it will be ready at time t+dt, where dt is an infinitesimal

increment of time.

This is right only on a infinitely small interval. But the model should

assume the real world. The real world is not a infinitely small interval.

The real world is the sum of the infinite number of the infinitely small

intervals. If the earth were to end in a infinitely small interval his

conclusion would be right.

This is the necessary condition for Poisson distribution. We can not apply

this to the model that does not premise a infinitely small interval. It is

right only to a infinitely small interval.

Someone might insist that in a continuous time model, the periods are too

short and we can apply Loury(1979)'s calculation. If h(x)dt were the exact

value of the probability, then this assertion could be right. But it is

not. I finish this note as making citation of Feller(1968. p. 162.)

3. The probability of exactly one failure in a small interval of time is

APPROXIMATELY proportional to the size of the interval.

4. The probability of n failure in a small interval is NEGLIGIBLE in

comparison with the probability of one failure in that interval.

********************************

With best regards,

Seonghun Cho

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

Subject:             Re: "The Business Stealing Effect is Wrong"

       Date:             Sun, 04 Oct 1998 17:41:26 -0700

      From:             cho <chose@ucs.orst.edu>

        To:             Gene Grossman <grossman@wws.princeton.edu>

        CC:            Helpman@ccsg.TAU.AC.IL

 References:             1

Dear Professor Grossman

Your (and all other's) confusion stems from the fact that you think lamda

as probability. In your models lamda can be more than 1. Is there any

probability more than 1? And your confusion has another origin that you

premise that lamda*dt converges to lamda when dt converges to 0. It is

nonsense. When dt converges to 0, lamda*dt converges to 0 not lamda.

*******

3. The probability of exactly one failure in a small interval of time is

APPROXIMATELY proportional to the size of the interval.

4. The probability of n failure in a small interval is NEGLIGIBLE in

comparison with the probability of one failure in that interval.

*********

You cannot assume the probability as lamda. Please read 3 again. Feller

does not say the probability is lamda. He says only "PROPOTIONAL."  You

can use 2*lamda or 1/2*lamda. There is no necessity to use lamda.

I think this mistake is Economics' mistake. We economists should correct

this mistake before any others do that. If we do not, We Economists will

be ashamed of ourselves forever.

With best regards,

Seonghun Cho

 

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Subject: Re: "The Business Stealing Effect is Wrong"

        Date: Mon, 5 Oct 1998 08:53:55 EDT

       From: "Gene Grossman" <grossman@wws.princeton.edu>

 Organization:WWS

         To:cho <chose@ucs.orst.edu>

Dear Mr. Cho,

Please do not send me any further email messages.

Sincerely,

Gene Grossman

The Business-Stealing Effect is Wrong.hwp

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