README.txt

Author: Klaus Reiner Schenk-Hoppé (klaus@iew.unizh.ch)
        http://www.iew.unizh.ch/home/klaus
Last update: February 1, 2000

This file gives a brief overview on the C and MATLAB files which have
been developed to carry out the numerical simulations in the paper
"Is T here a Golden Rule for the Stochastic Solow Growth Model?"
Working Paper No. 33, Institute for Empirical Research in Economics,
University of Zurich, January 2000 by Klaus Reiner Schenk-Hoppé. The
scripts are available at the web page
http://www.iew.unizh.ch/home/klaus/numerics

The data can be plotted with MATLAB http://www.mathworks.com


Compile the files with  gcc -lm  filename
to include the math library

At the end of this text you can find the calls to reproduce the figures of the paper.


Filename              Task                                          Output

golden_rule.c         calculate average consumption                 MATLAB file golden_rule.mat
                      as a function of the saving rate

                      Usage

                      a.out  production-function  s_min  s_max  steps  stochastic-case  pre-iterations  iterations

                      production-function  (1=Cobb-Douglas, 2=CES)
                      s_min  s_max  steps  (saving rate takes values in [s_min, s_max] on an equidistant grid with steps+1 vertices)
                      stochastic-case ( 0=deterministic, 1=production shocks, 2=stoch. population growth rate, 3=stoch. depreciation)
                      pre-iterations (number of iterations to get close to the sample path of the random fixed point)
                      iterations  (number of iterations to approximate average consumption)

                      start MATLAB and give the commands
                      load golden_rule.mat
                      plot(s,Ec)
                      to plot average consumption as a function of the saving rate


average_cons_prob.c   calculate average consumption                 MATLAB file average_cons_prob.mat
                      as a function of the transition probability p
                      of the stochastic parameter (two-state Markov
                      process with p_11 = p_22 = p)

                      Usage

                      a.out  production-function  stayprob_min  stayprob_max  steps  stochastic-case  pre-iterations  iterations saving-rate

                      production-function  (1=Cobb-Douglas, 2=CES)
                      stayprob_min  stayprob_max  steps  (transition probability p_11 = p_22 = p in [stayprob_min, stayprob_max] on an equidistant grid with steps+1 vertices)
                      stochastic-case ( 0=deterministic, 1=production shocks, 2=stoch. population growth rate, 3=stoch. depreciation)
                      pre-iterations (number of iterations to get close to the sample path of the random fixed point)
                      iterations  (number of iterations to approximate average consumption)
                      saving-rate  (fixed in (0,1))

                      start MATLAB and give the commands
                      load average_cons_prob.mat
                      plot(stayprob,Ec)
                      to plot average consumption as a function of the transition probability p_11 = p_22 = p


dyn_ineff_cond.c      check condition (10) in Section 5             stderr and MATLAB file dyn_ineff_cond.mat
                      the saving rate has to be
                      the golden rule saving rate!

                      Usage

                      a.out  production-function  s_min  s_max  steps  stochastic-case  pre-iterations  iterations

                      production-function  (1=Cobb-Douglas, 2=CES)
                      s_min  s_max  steps  (saving rate takes values in [s_min, s_max] on an equidistant grid with steps+1 vertices)
                      stochastic-case ( 0=deterministic, 1=production shocks, 2=stoch. population growth rate, 3=stoch. depreciation)
                      pre-iterations (number of iterations to get close to the sample path of the random fixed point)
                      iterations  (number of iterations to approximate average consumption)


                      the output on stderr is the
                      saving rate and the corresponding left-hand side of (10)
                      the condition (10) is satisfied if the expression is larger than or equal to zero


plot_cobb_douglas.m   MATLAB file  Call: plot_cobb_douglas(k1,k2)
                                   plots the function h with Cobb-Douglas production function and n = 0, delta = 0.5, alpha = 0.75, s = 0.75
                                   for the two values xi = 0.95 and xi = 1.05
                                   and the identity map


The figures in the paper can be generated as follows:

Figure 1 golen_rule 1 0.0 1.0 400 0 1000 10000      (deterministic)
golen_rule 1 0.0 1.0 400 1 1000 1000000    (production shocks)
golen_rule 1 0.0 1.0 400 2 1000 1000000    (stochastic population
growth rate) golen_rule 1 0.0 1.0 400 3 1000 1000000    (stochastic
depreciation rate)

(It is a good idea to calculate each stochastic case in 4 steps, e.g.
 golen_rule 1 0.0 0.25 100 1 1000 1000000
 mv golen_rule.mat golden_rule_xi_1.mat
 and so forth, because run-time is quite long)

Figure 2 golen_rule 2 0.0 1.0 400 0 1000 10000      (deterministic)
golen_rule 2 0.0 1.0 400 1 1000 1000000    (production shocks)
golen_rule 2 0.0 1.0 400 2 1000 1000000    (stochastic population
growth rate) golen_rule 2 0.0 1.0 400 3 1000 1000000    (stochastic
depreciation rate)

Figure 3
(start MATLAB first)
plot_cobb_douglas(0,65000) gives the picture on the left
plot_cobb_douglas(35000,65000) gives the picture on the right

Figure 4 average_cons_prob 1 0.0 1.0 400 1 1000 2000000 0.75
(production shocks in {0.95,1.05})