Non-convex Adjustment Costs Research Articles

Caballero–Engel meet Lasry–Lions: A uniqueness result

In a Mean Field Game (MFG) each decision maker cares about the cross sectional distribution of the state and the dynamics of the distribution is generated by the agents’ optimal decisions. We prove the uniqueness of the equilibrium in a class of MFG where the decision maker controls the state at optimally chosen times. This setup accommodates several problems featuring non-convex adjustment costs, and complements the well known drift-control case studied by Lasry–Lions. Examples of such problems are described by Caballero and Engel in several papers, which introduce the concept of the generalized hazard function of adjustment. We extend the analysis to a general “impulse control problem” by introducing the concept of the “Impulse Hamiltonian”. Under the monotonicity assumption (a form of strategic substitutability), we establish the uniqueness of equilibrium. In this context, the Impulse Hamiltonian and its derivative play a similar role to the classical Hamiltonian that arises in the drift-control case.

Heterogeneity in the effects of uncertainty shocks on labor market dynamics and extensive vs. intensive margins of adjustment

The real option value theory posits that non-convex adjustment costs pertaining to a firm's input are central to comprehending the consequences of increased uncertainty. This paper leverages the diversity observed at both sectoral and country levels in the degree of irreversibility associated with hiring and firing, a critical factor generating what is commonly referred to as “wait-and-see” behavior in times of heightened uncertainty. Our empirical findings reveal two key insights. First, in alignment with the concept of second-moment shocks, uncertainty shocks predominantly influence the labor market through the extensive margin rather than the intensive margin. Second, the effects of uncertainty shocks exhibit pronounced heterogeneity across countries and industries, and the adverse employment effects (extensive margin) are amplified in a country with strict employment protection or in an industry characterized by a higher natural layoff rate, consistent with the real option theory.

Aggregate demand uncertainty outbreaks and employment hysteresis in G7 countries

The slow recovery following the recent financial crisis in many developed countries, and the predictable long lasting economic effects of the Covid-19 pandemic have raised a new interest on the topic of employment hysteresis. In the presence of hysteresis there is no predetermined long-run equilibrium level of aggregate employment. As the economic system is not self-adjusting toward a unique equilibrium, timely, and sustained expansionary macroeconomic policies should be applied to mitigate the impact of negative shocks. The purpose of this paper is to uncover hysteresis effects in the macrodynamics of employment along with variations in its intensity that may result from outbreaks in aggregate demand uncertainty. We estimate a switching employment equation based on the play model of hysteresis, which describes a dynamic process whereby non-convex adjustment costs and uncertainty create intervals of weak reaction of employment to small changes in forcing variables, but spurts in the reaction to large demand shocks. As a novel feature, the estimation allows the presence of structural breaks in the value of the switching parameter of the employment equation due to aggregate demand uncertainty outbreaks. We have concluded that hysteresis effects increased in general in crisis periods associated to outbreaks of uncertainty in aggregate demand.

Hysteresis in the Dynamics of Employment by Activity Sector

ABSTRACT Hysteresis, referring to the property of a system whereby some temporary shocks cause permanent effects, has showed to be important to explain the dynamics of aggregate employment. What is not yet addressed properly in the literature is the differentiation of hysteresis effects according to activity sectors. This subject is important in order to understand whether severe recessions, like the one that followed the COVID-19 pandemic with its recognized heterogeneous immediate effects at the sectoral level, have permanent effects, and prospectively for applying adequate stabilizing fiscal and monetary policies, and possibly other specific measures, to prevent excessive market shocks even if they are perceived to be temporary. For this purpose, we apply the play hysteresis model, which describes a dynamic process whereby non-convex adjustment costs create intervals of weak reaction of employment to forcing variables, and spurts in employment in reaction to large or cumulative small labour demand shocks. The model is implemented by means of a switching employment equation. The switching parameter is interpreted as an ‘employment band of inaction’ that summarizes the magnitude of the hysteretic effects. We have found significant hysteresis effects in the employment dynamics across sectors, and these are especially important for industry.

A Note on nonconvex adjustment costs in lumpy investment models: Mean versus variance

AbstractThis paper revisits the canonical assumption of nonconvex capital adjustment costs in lumpy investment models as in Khan and Thomas [(2008) Econometrica 76(2), 395–436], which are assumed to follow a uniform distribution from zero to an upper bound, without distinguishing between the mean and the variance of the distribution. Unlike the usual claim that the upper bound stands for the size (represented by the mean) of a nonconvex cost, I show that in order to generate an empirically consistent interest elasticity of aggregate investment, both a sizable mean and a sizable variance are necessary. The mean governs the importance of the extensive margin in aggregate investment dynamics, while the variance governs how sensitive the extensive margin is to changes in the real interest rate. As a result, both the mean and the variance are quantitatively important for aggregate investment dynamics.

Nonconvex Adjustment Cost in Lumpy Investment Models: Mean versus Variance

This paper revisits the canonical assumption of nonconvex capital adjustment costs in lumpy investment models as in Khan and Thomas (2008), which are assumed to follow a uniform distribution from zero to an upper bound, without distinguishing between the mean and the variance of the distribution. Unlike the usual claim that the upper bound stands for the size (represented by the mean) of a nonconvex cost, I show that in order to generate an empirically consistent interest elasticity of aggregate investment, both a sizable mean and a sizable variance are necessary. The mean governs the importance of the extensive margin in aggregate investment dynamics, while the variance governs how sensitive the extensive margin is to changes in the real interest rate. As a result, both the mean and the variance are quantitatively important for aggregate investment dynamics.

Hysteresis and sources of aggregate employment inertia

Abstract It is widely recognized that aggregate employment dynamics is characterized by hysteresis. In the presence of hysteresis, the long run level of employment instead of being unique and history-independent, depends on the adjustment path that is taken, which includes the monetary and fiscal measures. It is thus important to study the presence of hysteresis in the macrodynamics of employment to understand whether the recession followed 2007s financial crisis will have permanent effects, and prospectively to conduct fiscal and monetary policies. The main contribution of this paper is to analyse the relative impact of the main sources hysteresis (non-convex adjustment costs, uncertainty and the flexibility of working time arrangements) to the width of the employment band of inaction. For that purpose, a switching employment equation was estimated from a computational implementation of the linear play model of hysteresis. From our results we found significant hysteresis effects in the aggregate employment dynamics caused by the presence of non-convex adjustment costs as uncertainty. We also found that the flexibility firms may have to adjust labour input by varying the number of hours of work per employee helps to mitigate the effect of uncertainty upon the band of inaction.

Estimating the Employment Band of Inaction with Multiple Breaks due to Labor Market Reforms

This paper proposes a new way of testing the effect of labor market reforms in the employment adjustment at the macro level. Following the approach to hysteresis based on the presence of non-convex costs of adjustment, a switching aggregate employment equation is estimated, with an unknown splitting factor, from a computational implementation of the linear play hysteresis operator. The play hysteresis operator describes a dynamics where non-convex adjustment costs create intervals of weak reaction of employment to small variations in forcing variables, while spurts in employment adjustment may occur as a consequence of a large, or cumulative small shocks. The main contribution of this paper is to extend an existing approach for the case where there are disruptive breaks, by accommodating changes in the value of the switching parameter of the employment equation whenever labor market reforms are present. Numerical experiments on the Portuguese economy are performed.

Firm Heterogeneity in Production-Based Asset Pricing: The Role of Habit Sensitivity and Lumpy Investment

I study the interaction between lumpy investment and asset prices in both time-series and cross-section. To this end, I work with a variant of habit sensitivity function introduced in Campbell & Cochrane (1999). The model produces 100% equity volatility of data by generating volatile marginal utility under the assumption of non-convex adjustment costs. Second, the model reproduces nearly 100% equity premiums of data because it assigns large weights on precautionary savings and constrained firms, respectively. Furthermore, the model can rationalise considerable size premiums as small firms absorb more productivity risks. Finally, the model matches key macroeconomic moments and the cross-sectional investment rate.

Really Uncertain Business Cycles

We propose uncertainty shocks as a new impulse driving business cycles. First, we demonstrate that uncertainty, measured by a number of proxies is strongly countercyclical. Second, we build a dynamic stochastic general equilibrium model that extends the benchmark neoclassical growth model along two dimensions. It allows for the existence of heterogeneous …rms with non-convex adjustment costs in both capital and labor and time-variation in uncertainty that is modeled as a change in the variance of innovations to productivity. We …nd that increases in uncertainty lead to large drops in economic activity. This occurs because a rise in uncertainty makes …rms cautious, leading them to pause hiring and investment. It also reduces the reallocation of capital and labor across …rms, leading to large falls in productivity growth. Finally, we show that because uncertainty makes …rms cautious it signi…cantly reduces the response of the economy to stimulative policy, leading to pro-cyclical policy multipliers.

Adjustment costs and threshold effects in factor demand relationships

ABSTRACTIt has been recently argued that producers may not respond to every input price change in the way that a linear factor demand model would predict. This lumpy response is due to adjustment costs that are inherent in the act of adjusting the mix of inputs applied in the underlying production technologies. This study aims to provide a solid conceptual framework for these nonlinearities in factor demand relationships. Industry-specific implications of convex and non-convex adjustment costs for the linearity of the factor demand relationships as well as price and substitution elasticities are explored. A two-regime threshold system of factor demand equations is estimated for several manufacturing industries in the United States. Empirical results suggest significant threshold effects in the factor demand relationships in most nondurable goods sectors. The size and the nature of thresholds depend upon industry characteristics, including input composition and (non)convexity of underlying adjustment costs. Complete matrices of price and substitution elasticities for each industry are derived using estimates of threshold factor demand systems. Discussion of two contrasting cases in greater detail sheds light on how the effect of price shocks on factor demand relationships varies across industries with different adjustment cost structures.

The Effects of Housing Adjustment Costs on Consumption Dynamics

Building on Flavin and Nakagawa (2008), this paper models household optimal consumption and portfolio selection when consumption services are generated by both non-durable consumption and by holding a durable good housing. Housing is illiquid in that a non-convex adjustment cost must be paid when it is sold. It is shown that optimal consumption of housing is not a constant fraction of wealth but instead depends on the ratio of wealth to housing and the price of housing. Households adjust housing infrequently, waiting for large wealth changes before adjustment. As in models without this adjustment cost, households adjust non-durable consumption each period. Unlike in frictionless models, non-durable consumption is not a constant fraction of wealth. For Particular parameters of the utility function and asset markets drawn from the literature, model simulations match aggregate consumption dynamics better than alternative frictionless models, even those with homes as assets. The simulations also predict differing responses of households with different fractions of their wealth in housing.

Investment–uncertainty relationship: differences between intangible and physical capital

ABSTRACTThis paper disentangles the effects of uncertainty in explaining the heterogeneity of firms’ investments. In particular, following Bloom [2007. “Uncertainty and the Dynamics of R&D.” American Economic Review 97 (2): 250–255], we test the role of uncertainty and liquidity constraints extending the model to include R&D, non-R&D intangibles, as well as physical capital. The analysis is performed on a large data set of Italian firms, covering both manufacturing and services sectors, as well as large and small firms. We show that non-convex adjustment costs affect different capital inputs in different ways, depending on their degree of firm-specificity. The results confirm the Bloom model: flow adjustment costs explain investment in R&D and, to a lesser extent, in non-R&D intangibles. However, it struggles to explain tangible investment plans because of the ambiguous effect of the stock adjustment costs.

Large open economies and fixed costs of capital adjustment

Capital reallocation creates excess volatility in investment in many two-country open economy models. Convex adjustment costs to capital have become a standard tool to deal with this. However, current microeconomic investment models feature non-convex adjustment costs as the dominant friction. This paper analyzes fixed costs to capital adjustment in a two-country business cycle model and finds that fixed costs – unlike in closed economies – dampen aggregate investment volatilities. Moreover, convex adjustment costs can serve as a stand-in for these fixed adjustment costs when one is interested in aggregate dynamics only. Yet, the mapping between fixed and quadratic adjustment costs co-depends on other model parameters.

Dynamics of labor demand: Evidence from plant-level observations and aggregate implications

This paper studies the dynamics of labor demand at the plant level to quantify labor adjustment costs. At the plant level, in contrast to time-series observations, the correlation of hours and employment growth is negative while hours and employment growth are about equally volatile. We specify and estimate the parameters of a plant-level dynamic optimization problem using simulated method of moments to match these plant-level observations. Our findings indicate that non-convex adjustment costs are critical for explaining plant-level observations on hours and employment adjustment.

Investment Dynamics with Information Costs

Investment in physical capital at the micro level is infrequent and large, or lumpy. The most common explanation for this is that firms face non-convex physical adjustment costs. The model developed in this paper shows that information costs make investment lumpy at the micro level, even in the absence of non-convex adjustment costs. When collecting and processing information is costly, the firm optimally chooses to do it sporadically and to be inactive most of the time. This behavior results in infrequent and possibly large capital adjustments. The model fits plant-level investment rate moments well, and it also matches some higher order moments of aggregate investment rates.

Investment Dynamics with Information Costs

Investment in physical capital at the microlevel is infrequent and large, or lumpy. The most common explanation for this is that firms face nonconvex physical adjustment costs. The model developed in this paper shows that information costs make investment lumpy at the microlevel, even in the absence of nonconvex adjustment costs. When collecting and processing information are costly, the firm optimally chooses to do it sporadically and to be inactive most of the time. This behavior results in infrequent and possibly large capital adjustments. The model fits plant-level investment rate moments well, and it also matches some higher order moments of aggregate investment rates.

Economic Uncertainty and the Effectiveness of Monetary Policy

This paper explores if economic uncertainty alters the macroeconomic influence of monetary policy. We consider several measures of U.S. economic uncertainty, and estimate their interaction eects with monetary policy shocks as identified through structural vector autoregressions. We find that monetary policy shocks aect economic activity considerably weaker when uncertainty is high, consistently with “real-options” eects suggested by models with non-convex adjustment costs. Investment responds two to five times weaker when uncertainty is in its upper instead of its lower decile. High U.S. uncertainty is associated with lower policy influence not only domestically, but in Canada too. JEL-codes: E30, E32, E37

What determines the Japanese firm investments: real or financial?

In this article, I test both the real and the financial frictions in the Japanese firm investments using structural approach. The real represents the nonconvex capital adjustment costs, and the financial means the financing constraints. These two factors have been studied for a long time, but rarely analysed simultaneously. Through this analysis, I find the following results. First, both these two factors affect Japanese firm investments. Second, convex adjustment costs parameter is estimated at a very small level. Third, this small convex adjustment costs lead to the model introduced in Wang and Wen (2012), which insists that the firm investments are determined by the upper bound of the borrowing constraints.

Lumpy Investment in Sticky Information General Equilibrium

In this paper, I introduce lumpy micro-level capital adjustment into a sticky information general equilibrium model. Lumpy adjustment arises because of inattentiveness in capital investment decisions instead of the more common assumption of non-convex adjustment costs. The model features inattentiveness as the only source of stickiness. I find that the model with lumpy investment yields business cycle dynamics which differ substantially from those of an otherwise identical model with frictionless investment and are much more consistent with the empirical evidence. These results therefore strengthen the case in favor of the relevance of microeconomic investment lumpiness for the business cycle.