The_Replacement_Effect_is_Wrong.hwp
AER's Referee Report.pdf
Abstract
Reinganum (1983, 1985) suggested the replacement effect. It has been accepted generally. But this common belief is wrong. Gilbert and Newbery (1984) and Yi (1995) say the replacement effect stems from Reinganum model's peculiarity. But Reingaum's replacement effect is only a calculation error. Reinganum considers three cases; the case of leader's success, the case of the challenger's success and the case of all firms' failure. The replacement effect stems from the third case. To consider the case of all firms' failure is a double calculation. It was already considered when the leader developed the present technology.
JEL Classification: O31
Keywords: replacement effect, innovation, endogenous growth.
1. Introduction
Now it is believed that, in the presence of uncertainty, the leader always invests less than the challengers in the patent race of a drastic innovation because of the replacement effect. But this common belief is wrong. We can see it by manifesting Reinganum(1985)'s illusion.
2. The Replacement Effect of Reinganum(1985)
Reinganum considers three cases; the case of leader's success, the case of the challenger's success and the case of all firms' failure. The replacement effect stems from the third case. But it is nonsense to consider the case of all firms' failure. There is no replacement effect if we do not consider the case of all firms' failure.
When the firm decides the amount of R&D investment it should consider the prize of R&D. In the situation of the consecutive drastic innovations, the prize of R&D can affected by the success time of the next innovation which is affected by the next race's R&D investment. The period of all firms' failure in the next race is the duration of technology. The case of all firms' failure is considered when the technology is developed. It means that all the participants expect the next race's R&D investment including their own R&D, i.e. they expect the duration of the technology they are now developing.
In Reinganum(1985), we don't need to consider the probability of all participants' failure. It was already considered when the participants of the previous race expected the duration of the technology they were searching. There is no need to reconsider it in the present race. The period of all participants' failure in the next race is the duration of the present technology.
The so-called replacement effect was already considered when the technology was developed. It cannot affect the present race.
There is no expectation about the next race's investment in Reinganum's model. Reinganum's model is not complete. So her conclusion, the replacement effect, is wrong. The prize of the patent race cannot be determined if there is no expectation about the amount of the next race's investment. The next race's investment determines the duration of the technology which is pursued in the present race.
Reinganum's replacement effect can be right if the stupid participants who consider the duration of technology is eternal, always win the patent race. The stupid leader considers the case of all firms' failure since the case is profitable to the stupid leader.
Let's think inanother way. The cause of the replacement effect in Reinganum(1985) is that the leader's present R&D investment has a negative effect on the leader's present value(the duration of the present technology). Because of this negative effect, the leader's marginal product of R&D is less than that of challenger's, and so the leader always invests less than the challenger.
But this conclusion is right only when the duration of the present technology gets shorter than the leader expected. The leader's R&D has no negative effect on her present value if the duration of the present technology is not shorter than the leader expected.
If all the participants had expected the duration of the technology in the previous race, then the leader(the participant of the previous race) has no need to reconsider that her or challengers' R&D investment of the present race has the negative effect on her present value(the duration of the present technology). It was expected already.
Reinganum's conclusion is right if we think only the first race since her model does not consider the expectation of the past. (Of course, this is wrong. We should consider the expectation of the past.) That's why her model seems to be fascinating. But the fascination cannot continue from the second race. From the second race her conclusion is not valid if we assume rational participants. To consider the case of all firms' failure is a double calculation. All the rational participants consider the duration of the technology they are searching for when they develop it. If one were to deny this, her conclusion should be nonsense.
3. Expectation and R&D Incentive
In the situation of the consecutive drastic innovations, the participants should expect the duration of the technology they are now developing, i.e. they should expect the next race's R&D amount. Without this expectation they cannot decide the amount of the present race's investment. Because there is this expectation, we cannot say whose incentive is greater ex ante. The leader and the challenger have the same incentive.
What if the leader's previous expectation is found incorrect ex post? Let's use Reinganum(1985)'s model and add to it expectation.
If
If
4. Conclusion
It is known that the leader has greater incentive than the challenger in a non-drastic innovation. So we can conclude that if it is uncertain whether new technology is non-drastic or drastic, then the leader's incentive is always greater than the challenger's incentive ex ante.
And I want to clarify that even if the leader's incentive is greater than the challenger's incentive, the leader's R&D investment can be less than that of the challenger's because the productivity of R&D can differ between the leader and the challenger.
The so-called creative destruction happens not because of leader's less incentive but because of uncertainty. Many endogenous growth models which assume that the leader has less incentive than the challenger lose their theoretical bases.
References
Gilbert, Richard J. and Newbery, David M. G. "Preemptive Patenting and the Persistence of Monopoly," American Economic Review, v72 n3 June 1982, pp. 514-26.
Gilbert, Richard J.; Newberry, David M. G. "Uncertain Innovation and the Persistence of Monopoly: Comment." American Economic Review, v74 n1 March 1984, pp. 238-42.
Reinganum, Jennifer F. "Uncertain Innovation and the Persistence of Monopoly," American Economic Review, v73 n4 September 1983, pp. 740-48.
Reinganum, Jennifer F. "Uncertain Innovation and the Persistence of Monopoly: Reply," American Economic Review v74 n1 March 1984, pp. 243-46.
Reinganum, Jennifer F. "Innovation and Industry Evolution," Quarterly Journal of Economics, v100 n1 February 1985, pp. 81-99.
Tirole, Jean The Theory of Industrial Organization, Cambridge, MA:MIT Press, 1988.
Yi, Sang-Seung "Uncertain Innovation and Persistence of Monopoly Revisited," Economics Letters v49 n3 September 1995, pp. 319-22.
************ 1.
Dear Professor Reinganum.
I wrote a note about ’the replacement effect.' I sent my note to AER. My
note was rejected. I conjecture the referee was you. I would like to
refute the referee report in this letter.
In referee report you said two possibilities. one is a simple
misunderstanding， and the other is an alternative assumption. I assume
the same model as Reinganum(l985). So I refute only your assertion that
I have a simple misunderstanding.
You say
"In fact the equilibrium value of the current race， which is Vw， is
determined by the current race’ s equilibrium investment， not the next
race’s investment. But the "prize" in the current race， which is
continuation value of Vw， is determined by the next race's investment.
If the author is confused and thinks Vw--or， more pointedly， the
expected (discounted) duration of the current stage -- is determined by
the next race's investment， this could perhaps explain why s/he does not
believe Reinganum's result. The expected (discounted) duration of the
current stage is most definitely determined by current investment"
My Refutation
You say "The expected (discounted) duration of the current stage is most
definitely determin어 by current investment." In fact current investment
determines the beginning time. But the ending time(i.e. the beginning
time of the next race) is determined by the next race's investment. So
the expected (discounted) duration of the current stage is most
definitely determined by current and next investment.
The prize of the patent race cannot be determined if there is no
expectation about the amount of the next race's investment. The next
race's investment determines the duration of the technology which is
pursu어 in the present race. The replacement effect was already
considered when the technology was developed. It cannot affect the
present race. In Reinganun1(l985) we don't need to consider the
probability of all participants' failure.
And what determines R&D is not Vw but the 'prize' of winning if we
distinguish between Vw and the ’prize’ as Reinganum insists.
I would be very pleased if you reply to my refutation.
Sincerely，
June 28. 1998.
Seonghun Cho
******************** 2.
July 3，1998
Dear Mr. Cho.
Thank you for your letter. In your paper， you say that "The root cause
of the replacement effect.... is that the leader's present R&D
investment has a negative effect on the leader's present value(the
duration of the present technology)." This is a correct assessment of
what occurs in my model. However， you do not believe this analysis is
correct， but I don't understand why.
You correctly point out that "The next race's investment determines the
duration of the technology which is pursued in the present race." An
immediate corollary of this is that the current race's investment
determines the duration of the technology which was pursued in the
previous race(and which is now being used for the duration of the
current race). In other words， the duration of the current race is
determined by the current investment， which governs the arrival time of
the next technology (the one which is currently being pursued).
In the second page of your letter， you say "current investment
determines the beginning time" of the current race. This is not correct;
the beginning time of the current race was the random date of discovery
of the technology currently in use， which was governed (stochastically)
by the investment rates in the previous stage. And the ending time (the
beginning of the next race) will be the random date of discovery of the
technology currently being pursued， which is governed (stochastically)
by the investment rates in the current stage.
I can only suggest that you do the analysis for yourself， perhaps
beginning with a single innovation as in my 1993 AER paper. See also the
paper by Lee and Wilde， who use the same formulation (perhaps their
development of the payoff functions is clearer than mine). With one
innovation， the only difference between my model and Lee and Wilde’ s is
that their is a flow revenue R in addition to the flow cost x. This is
sufficient to generate the replacement effect.
Sincerely，
Jennifer F. Reinganum
******************* 3.
Dear professor Reinganum
Thank you very much for your reply. But I still think you do not
understand my assertion.
You say "The duration of the current race is determined by the current
investment， which governs the arrival time of the next technology(the
one which is currently being pursued)."
You say only about the ending time of the current technology. But any
investment should consider the duration of the technology which it
pursues.
To determine the current investment， we should consider both the arrival
time of the next technology and the ending time of the next technology
which is determined by the next race's investment.
So the expected duration of the next technology is most definitely
determined by current and next investment.
The prize of the patent race cannot be determined if there is no
expectation about the amount of the next race's investment. The next
race's investment determines the duration of the technology which is
pursued in the present race. The replacement effect was already
considered when the technology was developed. It cannot affect the
present race. In Reinganum(l985) we don't need to consider the
probability of all participants' failure.
I say about EXPECTATION. You do not consider EXPECTATION.
Thank you very much.
Sincerely，
July 27 1998
Seonghun Cho
***************** 4.
Subject: Re: Replacement Effect
Date: Wed， 29 Jul 1998 09:42:59 -0500 (CDT)
From: reingajf@ctrvax. V anderbilt.Edu (Jennifer Reing anum)
To: cho <chose@ucs.orst.edu>
Dear Mr. Cho
The hazard function which governs the duration of the current
technology is a function only of current investment; that is， h (x)，
where x
is the investment rate in the current race. The ***optimal*** value of
current investment is (in equilibrium) a function of the other
parameters of
the model， including the continuation values of winning and losing the
current race (this is the expected discounted value of all the
subsequent races); that is， x* = f(vL， vW)， where vL is the continuation value
after losing the current race and vW is the continuation value after winning
the current race. The next race's investment affects the duration of the
current technology only through these continuation values， not directly
through the hazard function for the current race. Since no
precommitments can be made， these continuation values summarize all relevant
information about future investments， and are taken as given (not subject to choice)
in the current stage. I believe that these continuation values are the
expectations to which you refer. Yes， one needs to determine these
expectations in order to calculate the optimal current investment rate;
this is done through dynamic programming backwards from the "last" race.
Sincerely,
Jennifer F. Reinganum
******************* 5.
Dear professor Reinganum
You are right if the present leader is stupid leader. Stupid leader had
thought its present technology would be eternal when it develoPed new
technology. So the present stupid leader should consider the probabiliη
of 외1 participants' failure(duration of the present technology) now.
For you to be right， there should be stupid participants and they should
win the patent race always.
But we cannot premise stupid participants. We should premise rational
participants. Rational participants consider the duration of the
technology which they are pursuing. So they had already considered the
probability of all participants' failure when they developed new
technology.
In the situation of the consecutive drastic innovations， the
participants should expect the duration of the technology they are now
developing， i.e. they should expect the next race’s R&D amount. Without
this expectation they cannot decide the amount of the present race's
investment. Because there is this expectation， we cannot say whose
incentive is greater ex ante. The leader and the challenger have the
same incentive.
Let me give you a simple example.
Intel develops 286， 386， 486 ...... Let's assume that the present
technology is 286 and participants are pursuing 386. Intel had already
considered the duration of 286. Intel has no need to consider that its
investment for 386 has a negative effect to its profit from 286. Because
Intel had expected it. Intel expected the duration of 286 by expecting
the total(its and challenger's) investment for 386.
Thanks again for your kind reply.
Sincerely，
7. 30. 98.
Seonghun Cho
************************ 6.
Subject: replacement effect
Date: Tue， 04 Aug 1998 09:05:24 -0500 (CDT)
From: reingajf@ctrvax.Vanderbilt.Edu (Jennifer Reinganum)
To: chose@ucs.orst.edu
Dear Mr. Cho:
All of the participants in the game are fully rational. At each
stage， they base their investment in the current race on the expected
value
of the continuation game， which incorporates the expected future
durations
of the innovation they are now pursing and all subsequent innovations.
However， the duration of the current race is a function of current
investment (which is， in equilibrium， a function of the continuation
values). Dynamic programming is the method by which these expectations are
computed. I suggest that you write down a two-innovation sequence of patent
races and use dynamic programming to analyze the problem， beginning from the
end and working backward. Indeed， the effect can be found simply by
analyzing a one-innovation problem， if you assume that one of the firms
receives flow profits from a previous innovation (as in my AER 1984 paper).
Sincerely，
Jennifer F. Reinganum
************************* 7.
Dear professor Reinganum
If all of the participants in the game are fully rational， they have no need to
consider the probability of all participants' failure(duration of the present
technology). They had already considered the probability of all participants'
failure when they developed new technology.
The duration of the current race is a function of current and expected next
investment.
You say
********
I suggest that you write down a two-innovation sequence of patent races
and use dynamic programming to analyze the problem， beginning from the end
and working backward. Indeed， the effect can be found simply by analyzing a
one-innovation problem， if you assume that one of the firms receives flow
profits from a previous innovation (as in my AER 1984 paper).
********
I know what you are saying. But the present is the result of the past. You
do not consider the expectation of the past. I write again. If all of the
participants in the game are fully rational， they have no need to consider the
probability of all participants' failure(duration of the present technology) AGAIN.
Thanks.
Sincerely，
8.4.98.
Seonghun Cho
********************** 8.
Subject: About Replacement Effect
Date: Wed， 05 Aug 1998 07:24:27 -0700
From: cho <chose@ucs.orst.edu>
To: Jennifer Reinganum <reingajf@ctrvax.Vanderbilt.Edu>
References: 1
Dear professor Reinganum
What does the firm consider when it does R&D? Of course， the cost and
the benefit. What is the cost of R&D? The cost is the present value of the
whole investment of the development PERIOD. The benefit is the present value
of the whole profit of the technology's DURA TION. Instantaneous cost and
profit is not the things the firm considers.
So the duration of the current race is a function of current and expected
next investment.
Thanks.
Sincerely， Seonghun Cho
**********************************
I want to refute Reinganum's assertion more.
1. What is Vw in Reinganum's model?
In her paper p.85.
****
This is because the continuation values， Vw， Vl， are independent of actions taken in
the current stage.
***********
She said "Vw is continuation value and it is independent of actions taken in the current
stage."
In her first letter (referee report)
*********
"In fact the equilibrium value of the current race， which is VW， is determined by the
current race's equilibrium investment， not the next race's investment. But the "prize" in the
current race， which is continuation value of VW， is determined by the next race's
investment. If the author is confused and thinks VW --or， more pointedly， the expected
(discounted) duration of the current stage -- is determined by the next race’s
investment，
this could perhaps explain why s/he does not believe Reinganum's result. The expected
(discounted) duration of the current stage is most definitely determined by current
investment"
**************
She said "Vw is determined by the CURRENT race's equilibrium investment， not the
next race's investment." This is contradictory to her assertion that Vw is independent of
actions taken in the current stage.
And she said " Vw is the expected DURATION of the current stage." This is
contradictory to the fact that she call Vw continuation value in her paper.
In fact she is confused about Vw. Vw should be the prize of winning.
2.
In her third letter， she said
*************
The hazard function which governs the duration of the current
technology is a function only of current investment; that is， h(x)， where x
is the investment rate in the current race.
*******************
How does the hazard function govern the DURATION of the current technology?
This assertion is nonsense. The hazard function governs the beginning time of next
technology(ending time of the current technology). Hazard function governs the time not
the duration. Why don't you consider Reinganum’s wrong assertion. With only this one can
tell who is wrong.
********
The ***optimal*** value of
current investment is (in equilibrium) a function of the other parameters of
the model， including the continuation values of winning and losing the
current race (this is the expected discounted value of all the subsequent
races); that is， x* = f(vL， vW)， where vL is the continuation value after
losing the current race and vW is the continuation value after winning the
current race. The next race's investment affects the duration of the
current technology only through these continuation values， not directly
through the hazard function for the current race. Since no precommitments
can be made， these continuation values summarize all relevant information
about future investments， and are taken as given (not subject to choice) in
the current stage. I believe that these continuation values are the
expectations to which you refer. Yes， one needs to determine these
expectations in order to calculate the optimal current investment rate; this
is done through dynamic programming backwards from the "last" race.
**********
I cannot understand what she says. She tries to protect her conclusion by making Vw
mysterious. I cannot understand her mysterious Vw.
Backward induction cannot deny the simple principle: All rational participants consider
the duration of the technology they are searching for. on the contrary backward induction
means that all rational participants consider the duration of the technology they are
searching for.
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