RBC Model Simulation Results: Impulse Responses to Shocks - How do RBC model economies behave in response to shocks? - Good examples of this type of exercise: Heijdra Foundations of Modern Macroeconomics Ch. 15 Section 15.5 Romer Advanced Macroeconomics Ch. 5, Section 5.6 McCandless The ABCs of RBCs Ch. 6, Section 6.5 - The results in these sources are derived using the same type of method as Uhlig: start with a version of the Ramsey model, derive first-order conditions and the steady-state, create a log-linearized version of the model, find the law of motion for the model and then generate the impulse responses. - But the models are slightly more complicated versions of the Uhlig’s model. - What do the more typical first generation RBC models add? - Labour - Government - Notation: Y = output (GDP); Z = productivity; K = capital; N = employment; w = wages; r = interest rate I = investment; C = consumption; l = leisure FK = marginal product of capital  = depreciation rate FN = marginal product of labour
- Labour supply: marginal condition governing division of time between labour and leisure in each period. - leisure is a normal good: more leisure, less labour supply if more wealthy (i.e. if more lifetime resources) - intertemporal substitution stories (see MaCurdy; Lucas and Rapping): work more in periods when the wage is high. Firms: - produce and supply output. - demand capital and labour to produce output. e.g. higher productivity boosts input demand; higher input prices tend to decrease input demand. - link between productivity of capital (FK≡∂F/∂K) and the interest rate (r), i.e. FK-=r Capital accumulation: - reflects consumption and savings decisions of households and investment / capital demand of businesses. Response to shocks in these models: “In general, we can think of the effects of shocks as working through wealth and intertemporal substitution effects” Romer p. 214 - What shocks are typically examined? - Technology shocks the most common in the literature. - “technology shock” or “productivity shock”: same thing – a shift in the production function. - Also have government spending shocks in the Romer and Heijdra. - Shocks could be permanent or temporary. If temporary they may also differ in their persistence.
Federal Reserve Bank of Minneapolis Quarterly Review. “The match between theory and observation is excellent but far from perfect” “We ask whether these artificial economies display fluctuations with statistical properties similar to those which the American economy has displayed... They do.” Prescott (2004) views the models as a success: “conditional on labour supply elasticity close to 3, TFP shocks are the major contributor to fluctuations in the period 1954-1981 in the US” p. 383 (TFP – productivity) 3? 1% rise in wages raises labour supply by 3% (people must be very responsive to wages) - he also notes that this finding seems to be robust to a number of extensions. “We learned that business cycle fluctuations are the optimal response to real shocks. The cost of a bad shock cannot be avoided and policies that attempt to do so will be counterproductive ...” Prescott p. 389 - So supporters think the exercise says that Walrasian, competitive models with shocks can give results like actual cycles and that these results have big implications for policy. Basic RBC Model: Conclusions - Romer pp. 226-229. - RBC models: extend Ramsey model to allow for fluctuations - Microfoundations: