Does History Matter? Empirical Analysis of Evolutionary Versus Stationary Equilibrium Views of the Economy

Abstract

The evolutionary vision in which history matters is of an evolving economy driven by bursts of technological change initiated by agents facing uncertainty and producing long term, path-dependent growth and shorter-term, non-random investment cycles. The alternative vision in which history does not matter is of a stationary, ergodic process driven by rational agents facing risk and producing stable trend growth and shorter term cycles caused by random disturbances. We use Carlaw and Lipsey’s simulation model of non-stationary, sustained growth driven by endogenous, path-dependent technological change under uncertainty to generate artificial macro data. We match these data to the New Classical stylized growth facts. The raw simulation data pass standard tests for trend and difference stationarity, exhibiting unit roots and cointegrating processes of order one. Thus, contrary to current belief, these tests do not establish that the real data are generated by a stationary process. Real data are then used to estimate time-varying NAIRU’s for six OECD countries. The estimates are shown to be highly sensitive to the time period over which they are made. They also fail to show any relation between the unemployment gap, actual unemployment minus estimated NAIRU and the acceleration of inflation. Thus there is no tendency for inflation to behave as required by the New Keynesian and earlier New Classical theory. We conclude by rejecting the existence of a well-defined a short-run, negatively sloped Philips curve, a NAIRU, a unique general equilibrium with its implication, a vertical long-run Phillips curve, and the long-run neutrality of money.

This is a revised version of a paper presented at the 44th Annual Conference of the CEA May 28–30, 2010, Quebec City and the 13th ISS Conference 2010 in Aalborg, Denmark June 21–24, 2010

Modified and extended version from Journal of Evolutionary Economics 22(4), 735–766, Springer (2012).

Appendix: Summary of Carlaw and Lipsey (2011) Model

The fixed supply of the composite resource, R, is allocated by private price-taking agents in the consumption and applied R&D sectors and by a government that taxes the applied R&D and consumption sectors to fund pure research at an exogenously determined level.

The constraint imposed by the composite resource is:

$$ {R_t}=\sum\limits_{i=1}^I {r_t^i} +\sum\limits_{y=1}^Y {r_t^y} +\sum\limits_{x=1}^X {r_t^x} $$

(9)

1.1 The Applied R&D and the Consumption Sectors

The output of applied knowledge from each applied R&D facility, y, depends on the amount of the resource it uses and its productivity coefficient, which is the geometric mean of each ${{\left( {{G_{{{n_x}}}}} \right)}_t}$ term multiplied by its corresponding v term, as shown in (10).

$$ a_t^y=z_t^y{{\left[ {\prod\limits_{x=1}^X {{{{(\nu_{y,z}^{{{n_x}}}{{{(G_{{{n_x}}})}}_{t-1 }})}}^{{{\beta_x}}}}} } \right]}^{{\frac{1}{X}}}}{{(r_t^y)}^{{{\beta_{X+1 }}}}}, $$

(10)

$$ {\beta_x}\in (0,1]\kern0.5em \forall x\in X,\kern0.5em {\beta_{X+1 }}\in (0,1) $$

where $z_t^y$ is drawn from a Normal distribution with mean 1 and variance 0.2.

The stock of applied knowledge generated from each facility accumulates according to:

$$ A_t^y=a_t^y+(1-\varepsilon )A_{t-1}^y, $$

(11)

where $\varepsilon \in (0,1)$ is a depreciation parameter.

In the consumption sector, we make the simplifying assumptions (1) that there are the same number of applied R&D facilities and consumption industries, Y = I, and (2) that the knowledge produced in each of the facilities, y, is useful only in the one corresponding consumption industry, i. The production function for each of the I industries in the consumption sector is then expressed as follows:

$$ c_t^i=z_t^i{{(\mu A_{t-1}^y)}^{{{\alpha_y}}}}{{(r_t^i)}^{{{\alpha_{Y+1 }}}}},{\alpha_y}\in (\text{0,1}]\ \forall y\in Y,\ {\alpha_{Y+1 }}\in (0,1)\mathrm{and}{\it i}=y $$

(12)

where $z_t^i$ is drawn from Normal distribution with mean 1 and variance 0.06

1.2 The Pure Knowledge Sector

There are X labs each producing one class of pure knowledge that leads to the occasional invention of a new version, n _x , of that class of GPT. The productivity coefficient in each lab is the geometric mean of the various amounts of the Y different kinds of applied knowledge that are useful in further pure research (one for each applied R&D facility and each raised to a power σ _y ). The output of pure knowledge in lab x, $g_t^x$, is a function of the geometric mean of the various amounts of applied knowledge produced from the Y facilities doing applied R&D and the amount of the composite resource devoted to that lab.

$$ g_t^x={{\left[ {\prod\limits_{y=1}^Y {{{{\left( {(1-\mu )A_{t-1}^y} \right)}}^{{{\sigma_y}}}}} } \right]}^{{\frac{1}{Y}}}}{{\left( {\theta_t^xr_t^x} \right)}^{{{\sigma_{Y+1 }}}}},\quad {\sigma_y}\in (0,1],\kern0.5em \forall\ y\in Y\ \mathrm{and}\ {\sigma_{{\it Y}+1 }}\in (0,1). $$

(13)

The stocks of potentially useful knowledge produced by each of the X labs accumulate according to:

$$ \Omega_t^x=g_t^x+(1-\delta )\Omega_{t-1}^x $$

(14)

where $\delta \in (0,1)$ is a depreciation parameter.

New GPTs are invented infrequently in each of the X labs and their invention date is determined when the drawing of the random variable $\lambda_t^x\geq \lambda^{*x }$. For simplicity, we let the critical value of lambda for each of the X labs be the same: $\lambda^{*x }=\lambda^{*}\ \forall\ x\in X$. When at any time, t, $\lambda_t^x\geq {\lambda^{*}}$, indicating that a new version of class-x GPT is invented, the index ${t_{{{n_x}}}}$ is reset to equal the current t, and n _x is augmented by one.

Here we alter the arrival condition to make it a function of endogenous behaviour as follows. At any point in time, t, $\lambda_t^x\geq \frac{{{\lambda^{*}}}}{{\left( {\sum\limits_{{\tau =\tau last}}^t {\sum\limits_{y=1}^Y {\left( {r_{\tau}^y} \right)} } } \right)}}$,where $\tau last$ is the date that the last GPT of any class arrived in the economy.

Agents make their adoption decisions with incomplete information. In each applied R&D facility the only ν that agents expect to change is the one associated with the challenging x-class GPT, so, we can compare the productivities for any of the y facilities by simply comparing the $v_{y,z}^{{{(n-1)_x}}}{{\left( {{G_{{{(n-1)_x}}}}} \right)}_{{{t_{{{n_x}}}}}}}$ that would result if the incumbent were left in place with the $\bar{v}_{y,z}^{{{n_x}}}{{\left( {{G_{{{n_x}}}}} \right)}_{{{t_{{{n_x}}}}}}}$ that is expected to result if the challenger were adopted. This comparison is made in each of the Y applied R&D facilities at time $t={t_{{{n_x}}}}$ so the test, stated generally for all applied R&D facilities, is:

$$ \left[ {\bar{v}_{y,z}^{{{n_x}}}{{{\left( {{G_{{{n_x}}}}} \right)}}_{{{t_{{{n_x}}}}}}}} \right]\geq \left[ {v_{y,z}^{{{(n-1)_x}}}{{{\left( {{G_{{{(n-1)_x}}}}} \right)}}_{{{t_{{{n_x}}}}}}}} \right]\mathrm{for}\ \mathrm{each}y\in \left[ {1,{\it Y}} \right]. $$

(15)

If the test is passed, the new GPT is adopted in facility y.

The evolving efficiency with which the GPT delivers its services is shown in (16) below.

$$ {{\left( {{G_{{{n_x}}}}} \right)}_t}={{\left( {{G_{{{(n-1)_x}}}}} \right)}_{{{(t-1)_{{{n_x}}}}}}}+\left( {\frac{{{e^{{\tau +\gamma (t-{t_{{{n_x}}}})}}}}}{{1+{e^{{\tau +\gamma (t-{t_{{{n_x}}}})}}}}}} \right)\left( {{\psi_t}\Omega_{{{t_{{{n_x}}}}}}^x-{{{(G_{{{(n-1)_x}}})}}_{{{(t-1)_{{{n_x}}}}}}}} \right), $$

(16)

where

$$ {\psi_t}=\frac{\displaystyle{{e^{{{{{n_t}}}\big/{X}}}}}}{{10+{e^{{{{{n_t}}}\big/{X}}}}}} $$

and n _t is the total number of GPT arrivals in the economy up to date t.

The equation shows the efficiency of the GPT, ${{\left( {{G_{{{n_x}}}}} \right)}_t}$, increasing logistically as the full potential of the GPT is slowly realized. ${t_{{{n_x}}}}$ is the invention date of the version n _x , of the class-x GPT, $\Omega_{{{t_{{{n_x}}}}}}^x$ is the full potential productivity of the new version of GPT x, ${{\left( {G_{{{(n-1)_x}}}} \right)}_{{{t_{{{(n-1)_x}}}}}}}$ is the actual productivity of the version that it replaced, evaluated at the time at which that earlier version was last used, ${t_{{{(n-1)_x}}}}$ and γ and τ are calibration parameters that control the rate of diffusion. The evolution of efficiency proceeds as follows. Initially, since ${t_{{{n_x}}}}=t$ (and because γ is very small, 0.07 in our simulations), the value of the efficiency coefficient is close to zero so that the initial productivity of the challenging GPT is close to that of the incumbent. As t increases over time the value of the efficiency coefficient approaches unity so that the GPT’s productivity approaches its full potential.

In the subsequent periods, the test in (15) is modified to note the productivity changes that occur over time:

$$ \left[ {\bar{v}_{y,z}^{{{n_x}}}{{{\left( {{G_{{{n_x}}}}} \right)}}_t}} \right]\geq \left[ {v_{y,z}^{{{(n-1)_x}}}{{{\left( {{G_{{{(n-1)_x}}}}} \right)}}_t}} \right] $$

(15′)

for each y ∈ [1, Y] that has not yet adopted GPT ${G_{{{n_x}}}}$.

1.3 Resource Allocation

As we have already noted, in the pure knowledge sector the government pays for and allocates a fixed amount of the generic resource, R, to each of the pure knowledge producing labs. Producers in the applied R&D and consumption sectors maximize their profits each period taking prices as given.³¹ The prices for output from the I consumption industries are derived from the maximization of an aggregate utility function, which we assume is additively separable across the I consumption goods.

$$ U={\sum\limits_{i=1}^I {\left( {{c^i}} \right)}^{{{\phi^i}}}}\ \mathrm{and}\ {\phi^{\it i}}={\phi^{{\it i^{\prime}} }}=1,{\it i}\ne {\it i}^{\prime}\forall {\it i},{\it i}^{\prime}\in {\it I} $$

(17)

Maximizing this utility function and rearranging the first order conditions (FOCs) yields:

$$ \frac{{M{U^{i=1 }}}}{{M{U^{{i\ne 1}}}}}=\frac{{{P^{i=1 }}}}{{{P^{{i\ne 1}}}}}=\frac{{{\phi^{i=1 }}{{{\left( {{c^{i=1 }}} \right)}}^{{{\phi^{i=1 }}-1}}}}}{{{\phi^{{i\ne 1}}}{{{\left( {{c^{{i\ne 1}}}} \right)}}^{{{\phi^{{i\ne 1}}}-1}}}}} $$

(18)

Since ${\phi^i}=1\kern0.5em \forall \kern0.5em i\in I$ it follows that ${P^{i=1 }}={P^{{i\ne 1}}}$, i.e., the relative prices of all consumptions goods are unity.

We assume a competitive equilibrium in the market for the composite resource. This implies that it earns the same wage, w, regardless of where it is allocated.

Each consumption industry maximizes its profits taking the price of its consumption output, P ⁱ, and the prices of its inputs, composite resource, w, and applied knowledge, P ^y, as given. Profits are expressed as:

$$ {\pi^i}={P^i}{c^i}-w{r^i}-{P^y}{A^y} $$

(19)

Profit maximization yields the following FOCs in each of the I consumption industries:

$$ \begin{array}{lll} {P^i}mp{r^i}-w=0 \hfill \\{P^i}mp{A^y}-{P^y}=0 \end{array} $$

(20)

where mp represents marginal product. From the first FOC, the assumption the P ⁱ = 1, and the definition of the production function for industry i we get:

$$ {r^{i* }}={{\left[ {\frac{{{\alpha_{Y+1 }}}}{w}{{{\left( {\mu {A^y}} \right)}}^{{{\alpha_y}}}}} \right]}^{{\frac{1}{{1-{\alpha_{Y+1 }}}}}}}, $$

(21)

which is the reduced form expression for the demand for the composite resource in each consumption industry, i.

From the combination of both FOCs from the profit function for consumption industry i and the definition of the production function we get:

$$ \frac{w}{{{P^y}}}=\frac{{{\alpha_{Y+1 }}}}{{{\alpha_y}}}\frac{{{A^y}}}{{{r^i}}} $$

which implies that:

$$ {P^{y* }}=\frac{{{\alpha_y}w}}{{{\alpha_{Y+1 }}{A^y}}}{{\left[ {\frac{{{\alpha_{Y+1 }}}}{w}{{{\left( {\mu {A^y}} \right)}}^{{{\alpha_y}}}}} \right]}^{{\frac{1}{{1-{\alpha_{Y+1 }}}}}}} $$

(22)

Each applied R&D facility maximizes profits taking the price of its applied knowledge output, P ^y, and the composite resource, w, as given. The pure knowledge input in the form the currently adopted set of X GPTs is provided freely to the applied R&D facilities by the government financed labs. Profits are expressed as:

$$ {\pi^y}={P^y}{a^y}-w{r^y} $$

(23)

Maximization of the profit function and algebraic manipulation yields the following FOC:

$$ {P^y}mp{r^y}-w=0 $$

The demand for the composite resource from each of the Y applied R&D facilities is thus:

$$ {r^{y* }}={{\left[ {{\beta_{X+1 }}{{{\left[ {\prod\limits^X {{{{(v_{y.z}^{{{n_x}}}{{{({G_{{{n_x}}}})}}_t})}}^{{{\beta_x}}}}} } \right]}}^{{\frac{1}{X}}}}\frac{{{P^{{{y^{*}}}}}}}{w}} \right]}^{{\frac{1}{{1-{\beta_{X+1 }}}}}}} $$

(24)

With these resource demand equations we now have a complete description of the allocation of the composite resource across the three sectors.