Quadratic Adjustment Costs Research Articles

SOEs reform and capital efficiency in China: A structural analysis

This paper investigates the effect of state-owned enterprises reform, a policy phrased as “grasping the large, letting the small go”, on firms’ capital efficiency in Chinese industries from 1998–2007. First, we present several stylized facts on investment rates in state and private firms. Second, a dynamic programming problem is proposed and key structural parameters are recovered through simulated moment matching method, so the estimated dynamic model is able to replicate the stylized facts that are directly observable from the firm-level data. Our quantitative analysis shows that the conversion of state firms into private ones reduces capital adjustment costs. Particularly, state firms’ quadratic adjustment cost declines significantly almost by half, and the fixed cost decreases slightly. These findings are robust in various specifications. Hence, the reform in state firms leads to increased capital efficiency. Last, the counterfactual analysis suggests that state and private firm’s output would increase about 9.60% and 1.87% if the capital adjustment costs in state firms were lowered to the same levels in private firms.

Investment dynamics and capital distortion: State and non-state firms in China

This paper studies investment dynamics in Chinese manufacturing firms. The analysis estimates capital adjustment costs and uncovers capital distortion in state and non-state firms. There is strong evidence of quadratic adjustment cost and distortion in capital price for both types of firms. The capital distortion is a major source of capital misallocation in Chinese firms. Completely removing the distortion would increase aggregate total factor productivity (TFP) by 18–29%.

Price-setting with quadratic adjustment costs: Experimental evidence

We test the price-setting behavior of firms using the Rotemberg (1982) model in order to explain puzzles in the New Keynesian Phillips curve (NKPC). For our tests, we conducted experiments that adapt the model into an individual decision-making problem. We find systematic deviations in price-setting according to the subjects’ degree of information acquisition. Subjects rarely make use of past information. On the other hand, subjects that decide to acquire relatively little information about future desired prices tend to overweight their own past set price when they set prices. We study the impact of this heterogeneous price-setting behavior for theoretically derived forward-looking Phillips curves. Our estimated NKPCs are in line with the empirical literature. The deviations from theoretical predictions in our NKPCs are driven by the less-informed subjects.

The Effect of Heterogeneous Wage Contracts on Macroeconomic Volatility in a Financially Fragile Economy

I build a small open economy (SOE) dynamic stochastic general equilibrium (DSGE) model to investigate the effect of a heterogeneous wage contract between regular and temporary workers on a macroeconomic volatility in a financially fragile economy. The imperfect financial market condition is captured by a quadratic financial adjustment cost for borrowing foreign assets, and the labor market friction is captured by a Nash bargaining process which is only available to the regular workers when they negotiate their wages with the firms while the temporary workers are given their wage which simply equals the marginal cost. As a result of impulse responses to a domestic productivity shock, the higher elasticity of substitution between two types of workers and the lower weight on the regular workers in the firm’s production process induce the higher volatilities in most variables. This is reasoned that the higher substitutability creates more volatile wage determination process while the lower share of the regular workers weakens their Nash bargaining power in the contract process.

The Effect of Heterogeneous Wage Contracts on Macroeconomic Volatility in a Financially Fragile Economy

I build a small open economy (SOE) dynamic stochastic general equilibrium (DSGE) model to investigate the effect of a heterogeneous wage contract between regular and temporary workers on a macroeconomic volatility in a financially fragile economy. The imperfect financial market condition is captured by a quadratic financial adjustment cost for borrowing foreign assets, and the labor market friction is captured by a Nash bargaining process which is only available to the regular workers when they negotiate their wages with the firms while the temporary workers are given their wage which simply equals the marginal cost. As a result of impulse responses to a domestic productivity shock, the higher elasticity of substitution between two types of workers and the lower weight on the regular workers in the firm’s production process induce the higher volatilities in most variables. This is reasoned that the higher substitutability creates more volatile wage determination process while the lower share of the regular workers weakens their Nash bargaining power in the contract process.

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Dynamic labor demand in China: public and private objectives

This article studies dynamic labor demand by private and public manufacturing plants in China. The analysis uncovers the objectives of public and private enterprises and estimates labor adjustment costs by ownership. Public plants maximize the discounted present value of profits without a soft budget constraint. There is strong evidence of quadratic and linear firing costs at the plant level. The higher quadratic adjustment costs of the public plants may reflect their internalization of social costs of employment adjustment. Domestic private plants and collective plants have about the same discount factor, much lower than state‐controlled plants.

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.

How non-traded goods may generate quasi-quadratic costs for capital adjustment

This paper shows that a two-tiered production structure with both traded and non-traded intermediate goods and non-traded final goods can generate a cost of capital adjustment that is very similar to the quadratic adjustment cost often assumed in single good macroeconomic models. This implies that while a quadratic loss function may seem like an ad hoc adjustment, it can be rationalized by sound theory from a more detailed model.

GENERAL FORMULATION FOR A MANUFACTURING OF DEFECTIVE SETUP WITH DIFFERENT ADJUSTMENT METHODS

Consider the problem of adjusting a machine that starts production after a defective setup operation. This setup adjustment problem was first studied by Grubbs (1954, 1983). A general formulation for setup adjustment problems is presented in this paper. The formulation unifies some well-known process adjustment schemes, including Grubbs’ harmonic and extended rules, adjustment methods based on stochastic approximation and recursive least squares, and a recent method on adaptive EWMA feedback controllers. The proposed formulation is Bayesian and based on a Kalman Filter. The formulation allows to show the equivalence of the setup process adjustment problem with a simple instance of what in the control engineering literature is called a Linear Quadratic Gaussian (LQG) controller. As an important byproduct, the LQG model allows to solve more complicated setup adjustment problems with readily available techniques. Extensions to cases when there are quadratic adjustment costs and when the problem is multivariate are discussed. The multivariate setup adjustment solution is illustrated with a multihead filling machine example.

Investment decisions with financial constraints. Evidence from Spanish firms

This paper analyses to what extent the rejection of the investment dynamics implied by the Euler equation model with quadratic and symmetric adjustment costs can be attributed to the fact that the investment behavior of some firms in some periods is financially constrained by the availability of internal funds. I use a hierarchy of finance model which assumes that internally generated finance for investment is available at a lower cost than external finance, and implies the existence of distinct financial regimes depending on the firm’s financial policy. I estimate the empirical investment equation derived from the model using GMM, taking into account the endogeneity of the selection and allowing for debt finance, imperfect competition and the existence of a possible measurement error in the user cost of capital. The empirical results suggest that the Euler equation model is not seriously misspecified for a sub-sample of firms pursuing a particular financial policy.

Estimating the Euler Equation for Aggregate Investment with Endogenous Capital Depreciation

This article looks at the empirical consequences of introducing endogenous capital depreciation in the standard neoclassical model with quadratic adjustment costs. To this end, we formulate an empirical specification that accommodates capital maintenance and utilization in the Euler equations for aggregate investment. The empirical estimates with data from the Canadian Survey on Capital and Repair Expenditures show that, in contrast to the existing literature, the performance of the Euler equations is improved when we account for the impact of variable capital depreciation.

The effects of environmental policies on the abatement investment decisions of a green firm

Abstract This paper focuses on environmental policies aimed at rising investment in pollution abatement capital. We assume that ecological uncertainty, i.e., uncertainty over the dynamics of pollution, affects firm investment decisions. Capital irreversibility is not postulated but endogenized using a quadratic adjustment cost function. Using this framework, we study the effects of environmental policies considering taxes on polluting inputs and subsidies to reduce the cost of abatement capital. Environmental policies promoted to enforce abatement capital may generate the unexpected result of reducing the abatement investment rate.

Pollution Externality and Pollution Abatement Capital: A Closed-Form Solution for the Investment Rate of a Green Firm with Uncertainty and Irreversibility

This paper focuses on environmental policies aimed at rising investment in pollution abatement capital. Capital irreversibility is not postulated but endogenized using a quadratic adjustment cost function. We assume that ecological uncertainty, i.e. uncertainty over the dynamics of pollution, affects firm investment decisions. Closed-form solutions for the investment and value of a green firm are derived, showing that irreversibility reduces its fundamental value. The effects of environmental policies are investigated considering taxes on polluting inputs and subsidies to reduce the cost of abatement capital. Environmental policies promoted to enforce abatement capital may generate the unexpected result of reducing the abatement investment rate.

Corporate Governance and Liquidity Constraints: A Dynamic Analysis

Rich panel data for a large and representative sample of Estonian firms are used to estimate the sensitivity of access to capital to differing ownership structures. This is done through explicitly modelling firm investment behaviour in a dynamic setting in the presence of adjustment costs, liquidity constraints and imperfect competition. We estimate Euler equations derived in the presence of symmetric and quadratic adjustment costs and both debt and equity constraints. Generalized Method of Moments (GMM) estimates confirm the importance of access to capital in determining investment rates and suggest that firms owned by insiders, especially non-managerial employees, are more prone to be liquidity constrained than others.

A Comment on the Economics of Labor Adjustment: Mind the Gap: Evidence from a Monte Carlo Experiment

This comment addresses a point raised in Russell Cooper and Jonathan Willis (2003, 2004), which discusses whether the “gap approach” is appropriate to describe the adjustment of production factors. They show that this approach to labor adjustment as applied in Ricardo J. Caballero, Eduardo Engel, and John C. Haltiwanger (1997) and Caballero and Engel (1993) can falsely generate evidence in favor of nonconvex adjustment costs, even if costs are quadratic. Simulating a dynamic model of firm-level employment decisions with quadratic adjustment costs and estimating a gap model from the simulated data, they identify two factors producing this spurious evidence: approximating dynamic adjustment targets by static ones, and estimating the static targets themselves. This comment reassesses whether the first factor indeed leads to spurious evidence in favor of fixed adjustment costs. We show that the numerical approximation of the productivity process is pivotal for Cooper and Willis's finding. With more precise approximations of the productivity process, it becomes rare to falsely reject the quadratic adjustment cost model due to the approximation of dynamic targets by static ones. (JEL E24, J3)

Dinâmica do emprego e custos de ajustamento na indústria do Rio Grande do Sul

O presente estudo tem como propósito fazer uma análise empírica da estrutura dos custos de ajustamento do emprego industrial usando dados do Brasil. As estruturas teóricas para custos de ajustamento do emprego encontradas na literatura podem ser agrupadas em custos convexos (que incluem a popular função quadrática) e não-convexos (como custos fixos). Seguindo o trabalho de Varejão e Portugal (2007), empregamos metodologias complementares para a identificação da estrutura de custos de ajustamento de modo inovador no Brasil. Primeiro, usando matrizes de transição entre regimes de emprego. Segundo, empregando modelos de sobrevivência, que são mais gerais que os modelos de matriz de transição Markoviana. Os resultados obtidos sugerem que os custos de ajustamento não-convexos têm mais apoio nos dados do que o modelo usual de custos de ajustamentos quadráticos.

Wage or price-based inflation? Alternative targets in optimal monetary policy rules

In this paper the optimality of a specific variant of monetary policy rules à la Taylor is tested within a general equilibrium monetary model with both nominal and real rigidities. The traditional Taylor rule is amended by the inclusion of the growth rate of nominal wage, or ‘wage inflation’. Nominal rigidities are inserted via quadratic adjustment costs for both prices and wages à la Rotemberg [1982. Sticky prices in the United States. Journal of Political Economy 90, 1187–1211] and Kim [2000. Constructing and estimating a realistic optimizing model of monetary policy. Journal of Monetary Economics 45, 329–359]. Cost of capital adjustment together with a positive steady state inflation rate allow the model to match the main empirical facts about US economy. The model is solved by using a second order approximation around the non-stochastic steady state, as in Kim et al. [2008. Calculating and using second order accurate solutions of discrete time dynamic equilibrium models. Journal of Economic Dynamics and Control 32 (11), 3397–3414]. The welfare metric is offered by the second order expansion of the utility function conditional to the non-stochastic steady state. The results show that wage inflation targeting is welfare improving when coupled with inflation targeting. Moreover, optimal monetary rules include also a positive coefficient for output targeting, as the need to smooth out quantity adjustments induced by real and nominal rigidities. Similar results occurs when both targets are in expected value one period-ahead. The model shows good in sample and out of sample properties.

General Equilibrium Model of Arbitrage Trade and Real Exchange Rate Persistence

Modelling of the physical characteristics of goods and geography can explain both the puzzling persistence and volatility in the deviations of the international relative prices and the real exchange rate (the PPP persistence puzzle). In a two-country, three-good general equilibrium model, arbitrage firms trade goods across borders using a linear transportation technology. Distance and product weights (their physical mass) determine the costs to arbitrage trade, while the differences in the endowments between countries create profitable trading opportunities. Tradability of goods is endogenous, in that only goods with a deviation from the law of one price in excess of their trade cost are traded. The adjustment of prices across borders is non-linear, with heterogeneous thresholds that depend positively on the weight of a product and distance { an empirical regularity. Aggregation of the law of one price deviations implies a smooth threshold non-linearity in the real exchange rate, justifying a reoccurring finding in the recent empirical literature. When stochastic endowments follow an AR(1) process calibrated to match the quarterly HP-filtered US and EU GDPs, and the aggregate trade costs consume 1.7% of the GDP, the half-life of deviation in the real exchange rate matches the persistence found in the data. A model with quadratic adjustment costs in the volume of trade is also capable of creating real exchange rate volatility, and so can explain the PPP puzzle entirely as a trade phenomenon.

History versus expectations in economic geography reconsidered

This paper studies global stability of spatial configurations in a dynamic two-region model with quadratic adjustment costs where rational migrants make migration decisions so as to maximize their discounted future utilities. A global analysis is conducted to show that, except for knife–edge cases with symmetric regions, there exists a unique spatial configuration that is absorbing and globally accessible whenever the degree of friction is sufficiently small, and such a configuration is characterized as the unique maximizer of the potential function of the underlying static model.