Interaction effects in the adjustment cost function of firms

The literature has found that interaction effects exist between capital and labour in the adjustment cost function of firms, but there is no consensus on whether these costs are positive or negative. Using a dynamic firm structural model where capital is broken up into buildings and machinery & equipment, this paper finds that part of this ambiguity can be directly tied to capital heterogeneity. Firms are found to enjoy negative costs between labour and machinery & equipment, and between labour and buildings, while they suffer from positive costs between buildings and machinery & equipment. When compared to a model with only capital and labour, the interaction cost is found to be positive, highlighting how neglecting capital heterogeneity can lead to a spurious result on its sign. I evaluate the importance of these interactions by simulating three shocks: an increase in uncertainty, an increase in the interest rate, and an increase in the wage rate. I uncover large differences in the steady state dynamics of each input that are directly attributable to the interaction effects in the adjustment cost function.