Understanding investment activity in an economy is not trivial. The erratic nature of firm level investment activity is somewhat of a mystery to me and it took me quite some time to get a vague idea of what could be the generating process behind such an erratic behavior. I think understanding capital adjustment costs was the key to understand why it can be rational for firms to invest in a spasmodic way. In this post I would like to shortly summarize part of what I learnt so far and list different types of capital adjustment costs found in the literature.

Convex-Adjustment Costs

Capital adjustment costs are assumed to be convex in traditional investment theory. To be precise, the costs of adjusting capital are believed to be convex in the quantity of capital to be adjusted. The literature usually assumes convex adjustment costs to be of quadratic nature. This implies that the cost of adjusting capital increase disproportionally faster than the amount of capital to be adjusted. Personally I think this assumption might be true for a certain range of investment, however, I believe that this assumption loses it validity in the upper range of investment, i.e. when investment to capital is very high. Regardless the validity, convex adjustment costs lower the correlation between investment and economic activity. In the absence of convex adjustment cost modelled investment activity is highly correlated with economic activity. However, empirically this correlation is rather low. Convex adjustment cost allow to model firm level investment data much closer to actual observed investment data.

Non-Convex Adjustment Costs

Non-convex adjustment costs represent fixed costs of installing new capital and are independent of the capital to be adjusted. Non-convex adjustment costs can be experienced in two ways. First, during the installation of new capacity it might not be possible to operate the existing production plants at full capacity. Consequently, adjusting capital causes costs to a firm in form of lower profitability of existing capacities during the time of the adjustment (usually assumed to be one period). Second, there might additionally arise some lump cost, which is independent of the level of activity in a firm. This non-convex adjustment cost depends on the level of existing capital and is intended to limit size effects. Overall, non-convex adjustment costs allow to model an overshoot in investment (Cooper and Haltiwanger, 2006). The fixed nature of the costs and its independence of the size of adjustment creates an incentive of firms to overshoot its target capacity at first and let it physically depreciate over time.

Transactions Cost

Transaction costs represent an additional form of adjustment costs. Transaction costs assume that the price of capital is not the same when investing and disinvesting. Instead of one price capital has a buying and a selling price, where the selling price is assumed to be below the buying price. In the literature this difference in prices is often referred to as irreversibility. The extreme case of irreversibility assumes a selling price of zero, implying that once capital is acquired it cannot be sold. Pindyck (1988) uses full irreversibility and uncertainty to model erratic firm level investment behavior. The presence of transaction costs influences firm investment behavior. First, it hampers investment activity during an economic upswing as firms are cautious and anticipating that disinvestment of excessive capacity comes at a cost eventually or might not even be possible. Second, transaction cost lower disinvestment in an economic downturn as capacities can only be sold at a discount.

Literature

Abel, A. B., & Eberly, J. C. (1999). The effects of irreversibility and uncertainty on capital accumulation. Journal of Monetary Economics, 44(3), 339-377.

Bloom, N. (2009). The impact of uncertainty shocks. econometrica, 77(3), 623-685.

Cooper, R. W., & Haltiwanger, J. C. (2006). On the nature of capital adjustment costs. The Review of Economic Studies, 73(3), 611-633.

Pindyck, R. S. (1988). Irreversible Investment, Capacity Choice, and the Value of the Firm. American Economic Review, 78(5), 969-85.