![[Graph logo]](http://www.business.auc.dk/evolution/graph.GIF)
|
Toward a Multiactivity Generalisation of the Nelson-Winter model |
|
|
Andersen's
|
AbstractThe paper proposes a multiactivity generalisation of the Nelson-Winter model, or the NW model, in order to turn the attention of evolutionary minded economists toward specialisation and exchange, the emergence of markets for intermediate goods, the specialisation of R&D, and other issues of multisectoral growth and development. The argument and the solution is presented in four steps. First, there is a discussion of some practical difficulties and core theoretical problems in relation to the standard NW model of Schumpeterian competition. The conclusion is that this model gives an ad hoc solution to the tendency of evolutionary models to produce monopoly and that is has not really confronted the `knife-edge' problems of the underlying Leontief technology. Thus there is still a need to confront what may be called the diversity paradox and the Leontief technology paradox of evolutionary modelling. Second, the paper develops a condensed version of the NW model that serves to highlight the theoretical problems and as a platform for the proposed generalisation. This version of the NW model, the LNW model, includes only labour and knowledge. With given technologies the LNW model shows standard replicator dynamics while it can also be used as a testbed for exploring different R&D regimes. Third, the bare bones of the multiactivity generalisation of the NW model, the MNW model, is presented. This presentation starts from firms that produce their intermediate goods by means of labour and knowledge. Then the focus turns to exchange in intermediate goods and the related problems of the specialisation of R&D. Fourth, the paper discusses the MNW model's partial solutions to the diversity paradox and the Leontief technology paradox as well as the possibilities of further developing and applying the MNW model.The paper
NW: Reconstructions of Nelson-Winter models In addition to section 2 of the NW2001 Conference paper, you can read the following:
LNW: The pure-labour version of the basic NW model In addition to section 3 of the NW2001 Conference paper, you can read the following:
The core of the programThe core of the LNW model is implemented as follows:
# MAIN LNW PROGRAM
for t from 1 to T do
# SHORT RUN
for i from 1 to n do
Q[i,t] := A[i,t]*(1-r[i])*L[i,t];
od;
Qtot := sum(Q[k,t], k = 1..n);
P := Ltot/Qtot;
for i from 1 to n do
pi[i,t] := P*Q[i,t] - L[i,t];
s[i,t] := Q[i,t]/Qtot;
S[i,t] := L[i,t]/Ltot;
od;
# NEW TECHNO
for i from 1 to n do
A_res[i] := 0;
od;
A_max := max(seq(A[i,t], i = 1..n));
A_mean[t] := A_mean[t-1]*(1 + phi);
for i from 1 to n do
if Method = fixed then
A[i,t+1] := A[i,t];
fi;
if Method = random then
A_res[i] := exp(stats[random,normald[ln(A[i,t]),sigma]]());
if A_res[i] > A[i,t] then
A[i,t+1] := A_res[i];
else
A[i,t+1] := A[i,t];
fi;
fi;
if Method = normal or Method = split then
# Research
lambda[i] := d*r[i]*L[i,t];
if stats[random,poisson[lambda[i]]]() > 0 then
if evalf(rand()/1000000000000) < rho then
A_res[i] :=
exp(stats[random,normald[ln(A[i,t]),sigma]]());
else A_res[i] := A_max;
fi;
fi;
# Technochoice
A[i,t+1] := max(A[i,t], A_res[i]);
fi;
od;
# NEW LABOUR
for i from 1 to n do
L[i,t+1] := L[i,t] + pi[i,t];
od;
od;
Running the programThe Maple program is run by a procedure call of the form
LNW(n, T, Variable, Seed, Device);
where n = the number of firms
T = the number of periods
Variable = the variable to be plotted or saved
Seed = the interger that starts a specific series of random numbers
Device = 'screen' or 'filename'
Other parameters are set within the program; experiments presuppose
that the following standards are changed:
alpha := 0.2; A_init := 0.16*m; d := 1.0; K := 0; Ltot := 100; r[0] := 0.05; rho := 1; sigma := 0.05; Method := normal; Simulation exercisesHere are some results produced with the above model implementation:Pure replicator dynamics
 Random-walk cumulation of productivities
 R&D-based cumulation of productivities
 Two firms with R&D and two without
 Firms that are both innovators and imitators
MNW: The multiactivity generalisation of the NW/LNW models In addition to section 4 of the NW2001 Conference paper, you can read the following papers. However, you should note that the model specifications of these additional papers differ significantly from the NW2001 paper. In the near future simulation programs will be added.
|
|
Maintained by Esben Sloth Andersen, email: esa@business.aau.dk. Revision: 09 August 2004, 13:34.
|
||