Technological-knowledge dynamics in lab-equipment models of quality ladders

Abstract

The Perpetual Inventory Model (PIM) assumes that, in each period, an arbitrary constant fraction of technological-knowledge stock is lost. We give a theoretical background to the PIM by showing that the technological-knowledge accumulation follows a dynamic process with an endogenous depreciation rate, which remains stable in steady state.

Notes

¹The specific way each innovation arrival impacts on λ depends on whether we consider a model with intersectoral spillovers (Aghion and Howitt, 1998, ch. 3) or not (Barro and Sala-i-Martin, 2004, ch. 7). In any case, we take the usual assumption that each entrant possesses the same R&D technology, specified such that I is constant across industries, that is, , and also constant over t along the balanced-growth path.

²We assume that entrants are risk-neutral and, thus, only care about the expected firm value.

³The assumption of constant returns in R&D activities, instead of decreasing returns as in, for example, Segerstrom and Zolnierek (1999), simplifies the analysis but does not change the results in any fundamental way.

⁴The values for λ, θ, ρ and α were set in line with previous work on growth and guided either by empirical findings or by theoretical specification. The values of the remaining parameters were chosen to calibrate the steady-state aggregate growth rate around 2.5%/year. The normalization of L to unity implies that all aggregate magnitudes can be interpreted as per capita magnitudes.

⁵Interestingly, this value corresponds to the average of the estimates provided by Caballero and Jaffe (1993) for the creative-destruction rate in the United States.