Convex Adjustment Costs Research Articles

A Comment on the Economics of Labor Adjustment: Mind the Gap: Rejoinder

Numerous papers in this literature have used these questions as motivation. Understanding the structure of labor adjustment costs is relevant any time a policy or forecasting question requires input on the properties of labor dynamics. Of course, for some policy questions, we are interested in the aggregate effects of policies. Hence understanding whether nonconvexities have implications for aggregate labor demand is crucial as well. In terms of the ongoing discussion over these questions, there seems to be agreement that the simple quadratic adjustment cost model is not an adequate representation of the costs plants face in adjusting the number of workers. From data displayed by Daniel Hamermesh (1989) and Caballero et al. (1997), hereafter CEH, one is certainly struck by both the inactivity of labor adjustment and the bursts of job creation and destruction at the plant level. That said, while these observations serve as evidence against a model which contains only quadratic adjustment costs, they do not directly identify a particular structure of adjustment costs at the plant level. Inspection of the adjustment patterns reported in CEH, though cast in terms of gaps, does provide some evidence of partial adjustment and thus suggests the presence of both convex and nonconvex adjustment costs. Further, Caballero and Engel (1993), hereafter CE, and CEH appear to have provided useful evidence on the second question: the nonlinearities they uncover in aggregated data suggest that nonconvexities at the plant level have aggregate implications.

Credit rationing, profit accumulation and economic growth

This paper studies how credit rationing affects endogenous growth when capital and debt are related to the firm's internal net worth, taken as collateral. The accumulation of firm's net worth determines the growth rate of capital and the growth rate of the economy. The relation between growth and interest rate is then negative without requiring convex adjustment costs on investment.

Asset prices and real investment

Firm investment activity and firm characteristics, particularly the market-to-book ratio or q, are functions of the state of the economy and therefore contain information about the dynamic behavior of stock returns. This paper develops a model of a production economy in which real investment is irreversible and subject to convex adjustment costs. During low-q (high-q) periods when the irreversibility constraint (constraint on the rate of investment) is binding, conditional volatility and expected returns on one hand, and market-to-book ratios on the other, should be negatively (positively) related. Empirical tests based on industry portfolios support these predictions for conditional volatility but not for expected returns.

Capital Heterogeneity: Does It Matter? Fundamental Q and Investment on a Panel of Italian Firms

We study the determinants of firms' investment decisions with heterogeneous-capital goods. We exploit a panel of small and medium-sized firms, which allows us to distinguish between purchases and sales of capital goods. We consider separately equipment and structures and test the hypothesis of convex adjustment costs. We extend the fundamental Q approach to the case of two capital inputs. The results show that the standard convex costs model performs well for equipment but not for structures. We find evidence of nonconvex adjustment costs in the case of structures.

Zeros and Lumps in Investment: Empirical Evidence on Irreversibilities and Nonconvexities

The objective of this paper is to investigate if and how capital adjustment departs from the smooth pattern implied by standard model based on convex adjustment costs. Using Norwegian micro data, we start by documenting the intermittent and lumpy nature of investment rates. We then present two pieces of econometric evidence on these issues. First, we estimate a discrete hazard model to determine the probability of having an episode of high investment, conditional on the length of the interval from the last high-investment episode. Second, we estimate a switching regression model that allows for the response of the investment rate to fundamentals to differ across regimes. In both cases we investigate the aggregate implications of our results.

An empirical analysis of lumpy investment: the case of US petroleum refining industry

This paper employs five econometric models to examine lumpy investment and investigates the investment behavior of the US petroleum refining industry. Firms in the industry are classified into three groups by their size. All three groups show zero investment, disinvestment and investment in accordance with economic conditions. The analysis finds the minimum amount of investment and disinvestment for each group, which suggests that the size of fixed costs of investment is substantial, regardless of firm size. However, small firms adjust capital stock more slowly than medium or large firms. The analysis also suggests the existence of a convex adjustment cost.

On the Invariance of the Rate of Return to Convex Adjustment Costs

The modified golden rule, which relates the rate of return on capital and the growth rate of the capital stock along long-run growth paths that maximize the utility of a representative infinitely lived consumer, is invariant to the introduction of convex capital adjustment costs. Therefore, along balanced growth paths in neoclassical optimal growth models with an exogenous long-run growth rate of capital, the rate of return is invariant to the introduction of convex adjustment costs, though the capital–labor ratio is reduced along such paths. In AK models, convex adjustment costs reduce the growth rate and rate of return on capital. Journal of Economic Literature Classification Number: E2.

Costly Reversible Investment With Fixed Costs

The analysis presented here applies a generalized version of the friction model to costly reversible investment with fixed costs of investment. The analysis investigates three U.S. industries: the computer and office equipment industry, the automobile industry, and the airline industry. Five different investment models are compared. Because some models are nonnested, the analysis employs Vuong's test of model selection. The analysis shows that the investment model with costly reversibility and fixed costs is the best among the models. In addition, the analysis suggests the existence of convex adjustment costs of investment.

'The Principle of Increasing Risk': Kalecki's investment theory revisited

This paper reformulates Kalecki's investment models based on 'the principle of increasing risk'. First, it is shown that in his model risk can be interpreted as a conditional probability of bankruptcy of a firm, or the 'hazard rate' in reliability theory. Secondly, a simple static Kaleckian investment model is developed based on this interpretation. In the model, a slightly modified Kaleckian optimality condition for investment holds. It is also shown that, as Kalecki correctly pointed out, the principle of falling marginal efficiency of capital (or investment) is not required to obtain a finite level of investment. Finally, I consider sequential investment in an intertemporal model. In this model, a modified version of the Kaleckian optimality condition determines investment. In addition, as Kalecki emphasized, his increasing risk limits the level of investment even without increasing and convex adjustment costs associated with investment, by which the finite rate of investment is derived in the macroeconomics literature.

Protectionist response to import competition in declining industries reconsidered

This paper reconsiders the political economy of protection in declining industries. I return to the Stigler–Peltzman specification of the political support function and show that this specification can be used to portray temporary protection and by assuming partially mobile capital with convex adjustment costs, realistic adjustment paths: protection is gradually reduced in response to the decline in the world price until protection is completely withdrawn. The decrease in endogenous protection is, however, not a direct consequence of the decrease in the world price as in the standard portrait of senescent industry protection. It is rather self-inflicted by the perspicacious owners of specific capital.

Time-To-Build and Convex Adjustment Costs

This paper incorporates time-to-build into the standard investment model with convex adjustment costs. The empirical Euler equation is estimated using a U.S. firm-level panel from Compustat. In spite of the introduction of time-to-build, the magnitude of the implied adjustment costs is unrealistically high. Exploiting another approach, I test directly the restrictions imposed by time-to-build on the investment equation. The results indicate that these restrictions cannot be rejected for five of the sixteen industries in the sample. Finally I show that time-to-build can explain approximately one-third of the variation in persistence of structure investment across four-digit industries.

Time-to-Build and Convex Adjustment Costs

Time-to-Build and Convex Adjustment Costs

Capital Heterogeneity: Does it Matter? Fundamental Q and Investment on a Panel of Italian Firms

In this paper we study the determinants of investment decisions at the firm level with heterogeneous capital goods. We exploit a newly developed panel dataset of small and medium-sized firms which allows us to distinguish between purchases, sales, and net acquisitions of capital goods. We distinguish between equipment and structures and test the assumption of convex adjustment costs. Since our firms are mostly unlisted, the standard Q model based on stock market valuation is no longer appropriate. Instead, we use the fundamental Q approach proposed by Abel and Blanchard (1986) and Gilchrist and Himmelberg (1995) and extend it to the case of several capital inputs. The results show that the standard convex costs model fits very well equipment and but not structures. We find evidence for non-convexities in the case of structures.

New Plants as Natural Experiments in Economic Adjustment: Adjustment Costs, Learning-By-Doing and Lumpy Investment

A large sample of new plants is studied to reveal detailed adjustment behavior for capital, labor and productivity. Once production has begun, capital adjusts almost as quickly as labor. Overall, capital adjustment is lumpy while labor follows a learning-by-doing model rather than a convex adjustment cost model. Plants are quite heterogeneous, however: convex adjustment costs appear important at small plants, but large plants exhibit lumpy investment and substantial investment in learning-by-doing. A positive association between plant productivity growth and wages (and also the change in wages) corroborates the importance of learning-by-doing. Also, learning-by-doing appears to influence the behavior of large plants subsequent to startup.

Vector rational error correction

Abstract Systems of forward-looking linear decision rules can be formulated as vector ‘rational’ error correction models. The closed-form solution of the restricted error corrections is derived, and a full-information estimator is suggested. The error correction format indicates that the assumptions of convex adjustment costs and rational expectations impose different types of a priori restrictions on the dynamic structure of the error corrections. An empirical model of the producer decision rule for capital investment illustrates that the data rejects dynamic restrictions imposed by a standard model of adjustment costs but supports a more general description of convex frictions.

History, coordination and optimality: some policy lessons

Within a two-sector dynamic framework with external economies in one sector (which give rise to the possibility of multiple equilibria) and convex adjustment costs, this paper provides a welfare ranlung of movements towards the two stable equilibria, solves for the optimal speed of industrialization and derives the shape of the social planner's optimal resource allocation path. These results show that one should be cautious in drawing policy implications from static models of coordination failures. Moreover, this paper also argues that a reduction in adjustment costs (e.g. through the provision of public education facilities) is an essential precondition for industrialization when the existing industrial base is thin.

Capital Adjustment Patterns in Manufacturing Plants

A common result from altering several fundamental assumptions of the neoclassical investment model with convex adjustment costs is that investment may occur in lumpy episodes. This paper takes a step back and asks “How lumpy is investment?” We answer this question by documenting the distributions of investment and capital adjustment for a sample of over 13,700 manufacturing plants drawn from over 300 four-digit industries. We find that many plants do undergo large investment episodes; however, there is tremendous variation across plants in their capital accumulation patterns. This paper explores how the variation in capital accumulation patterns vary by observable plant and firm characteristics, and how large investment episodes at the plant level transmit into fluctuations in aggregate investment.Journal of Economic LiteratureClassification Numbers: D24, L6, E22.

The Employment-Financing Nexus: Evidence from a Panel of West German Firms

The objective of the paper is to investigate the linkage between financial factors and employment decisions of West German firms. The underlying model is based upon rational expectations and convex adjustment costs. The time series, cross-section estimates for the period 1989–1994 are obtained using information on individual firms contained in business surveys. We find that financial constraints can indeed restrain the level of employment in small firms. On the contrary, there is no evidence that this result applies to larger firms as well.

Investment Facing Credit Rationing

The explicit expression of investment facing credit rationing and convex adjustment costs is derived. Three implications follow. First, the assumption of convex adjustment costs can be substituted by credit rationing to derive an investment function. Second, it explains how credit rationing acts as a ‘financial brake’ at the bottom of a slump, when investment demand is high and collateral is low. Third, it allows the explicit Lagrange multiplier related to credit rationing to be derived and misspecification in recent empirical work to be checked.

Exchange-rate-based inflation stabilization: The initial real effects of credible plans

This paper studies the initial effects of exchange-rate-based stabilization programs within a dynamic general equilibrium model of a small open economy in which inflation acts as a tax on intermediate transactions and capital accumulation is subject to convex adjustment costs and gestation lags. The model replicates the typical pattern of slow inflation convergence, sustained real exchange rate appreciation, trade balance deterioration, and expansion in domestic spending followed by a deflationary slowdown, without resorting to sticky prices, imperfect credibility, or adaptive expectations. Calibrated versions of the model are compared with the initial effects of the Argentine Convertibility Plan of April 1991.