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5.1. CALIBRATING THE ONE-SECTOR GROWTH MODEL 1390.20.1GDP0Consumption-0.1-0.2-0.3Investment-0.4-0.573 75 77 79 81 83 85 87 89 91 93 95Figure 5.1: US data (symbols) and trend (no symbols) from Hodrick-Prescott Þlter. Observations are quarterly per capita logarithms ofGDP, consumption, and investment from 1973.1 to 1996.4.The modelWe will work with a version of the King, Plosser, and Rebelo [83]model that abstracts from the labor-leisure choice. The consumer haslogarithmic period utility deÞned over the single consumption goodu(C) =ln(C). Lifetime utility is P ∞j=0 β j u(C t+j ), where 0 < β < 1isthe subjective discount factor.The representative Þrm produces output Y t , by combining laborN t , and capital K t , according to a Cobb-Douglas production function.Individuals are compelled to provide a Þxed amount of N hours of laborto the Þrm each period. Permanent changes to technology take placethrough changes in labor productivity, X t . The number of effectivelabor units is NX t . This part of technical change is assumed to evolveexogeneously and deterministically at a gross rate of γ = X t+1 /X t .A second component that governs technology is a transient stochastic