Adjustment Cost Model Research Articles

Dynamic adjustment cost models with forward‐looking behaviour

Summary In this paper we propose a new approach for dynamic decision problems where forward-looking agents choose a set of non-stationary variables subject to quadratic adjustment costs. It is assumed that expectations are computed by a cointegrated Vector Equilibrium Correction Model (VEqCM). The role of feedbacks from the decision to the explanatory variables on solution properties and modelling approach is discussed. We show that once the system of interrelated Euler equations stemming from the agent's optimization problem is embedded within the VEqCM, a switching algorithm based on Generalized Least Squares can be used to estimate and test the model. A labour demand model for two Danish manufacturing industries is investigated empirically.

Semi‐parametric Modelling of Investments in Heating Installations: The Case of the Dutch Glasshouse Industry

AbstractThis paper applies a semi‐parametric approach to estimating a generalised model of investments in heating installations. The results suggest that marginal costs of investments in heating installations increase quickly at small investment levels, whereas the increase slows down at higher investment levels. Therefore, standard parametric adjustment cost models are probably biased such that they underestimate the costs of small investments and overestimate the costs of large investments. Results also show that investments in heating installations are very responsive to changes in energy prices. Therefore, an energy tax may be an effective instrument to encourage investments in new energy‐saving heating installations.

Stochastic intertemporal duality: An application to investment under uncertainty

We present a duality concept for a class of stochastic dynamic optimization problems that especially includes models of investment under uncertainty. This concept allows us to derive explicit characterizations of optimal investment behavior from an adjustment cost model with expectations described by linear or nonlinear stochastic processes. It covers settings that are impenetrable with a direct approach, like expectations with a multimodal density or certain forms of non-convex technologies.

Determinants of the Time Series of Earnings and Implications for Earnings Quality*

AbstractThis paper examines whether differences in accrual accounting methods across balance sheet accounts influence the time‐series process of earnings. We define earnings quality as the responsiveness of earnings to shifts in permanent earnings and predict that responsiveness will increase in a firm's use of variable rate debt, where accruals move directly with shifts in interest rates. We also predict that responsiveness will decrease in a firm's investment in property plant and equipment because depreciation is largely predetermined and does not respond to shifts in opportunity costs. </P><P>To test these hypotheses, we regress earnings on lagged earnings and a proxy for permanent earnings (that is, the implied dividend annuity in lagged equity value). Within the context of an adjustment cost model, this regression captures the responsiveness of earnings by the coefficient on lagged price and by one minus the coefficient on lagged earnings. Consistent with this framework, we find the unconstrained estimated coefficients on these two variables to be negatively correlated. Furthermore, consistent with our hypotheses, we find that the coefficient on lagged earnings (lagged price) is positively (negatively) associated with the relative magnitude and life of fixed assets on the balance sheet and negatively (positively) associated with the relative magnitude of variable rate debt on the balance sheet.</P>

Multi-equational linear quadratic adjustment cost models with rational expectations and cointegration

In this paper the econometric analysis of linear quadratic adjustment cost models with rational expectations and cointegrated variables is extended to the multi-equational SET-UP and the case of second-order adjustment costs. The proposed method is based on the idea of nesting the system of interrelated Euler equations stemming from the intertemporal optimization problem within a cointegrated Vector Equilibrium Correction Model representing the agent forecast tool. Contrary to previous practise a likelihood-based procedure can be set out without appealing to numerical optimization algorithms. Cointegration and generalized least squares techniques can be used to estimate and test the model.

Asset returns and business cycles in models with investment adjustment costs

We show that adjustment cost models with labor supply can explain both asset returns and business cycle facts when adjustment costs penalize the changes of investment. This conclusion stands in contrast to results obtained in the literature with adjustment costs that penalize the changes of capital.

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.

Asset prices and business cycles with costly external finance

This paper asks whether the asset pricing fluctuations induced by the presence of costly external finance are empirically plausible. To accomplish this, we incorporate costly external finance into a dynamic stochastic general equilibrium model and explore its implications for the properties of the returns on key financial assets, such as stocks, bonds and risky loans. We find that the mean and volatility of the equity premium, although small, are significantly higher than those in comparable adjustment cost models. However, we also show that these results require a procyclical financing premium, a property that seems at odds with the data.

Measures of Fit for Rational Expectations Models

This survey provides a detailed description of some of the recent theoretical and empirical literature on rational expectations econometrics. The survey pays special attention to non–stationarity of the data, and to the various methods for evaluating rational expectations models that have been developed as alternatives to the classical statistical approach of testing overidentifying restrictions. These methods have become very popular and widely used in empirical research. We provide an illustration using Danish stock market data, and we summarize the many results obtained recently using these measures in areas as diverse as stock prices, the term structure of interest rates, exchange rates, consumption and saving, the balance of payments, tax–smoothing, hyperinflation, and linear quadratic adjustment cost models for inventories, labour demand, and money demand.

Asset Prices and Business Cycles with Costly External Finance

This paper asks whether the asset pricing fluctuations induced by the presence of costly external finance are empirically plausible. To accomplish this, we incorporate costly external finance into a dynamic stochastic general equilibrium model and explore its implications for the properties of the returns on key financial assets, such as stocks, bonds and risky loans. We find that the mean and volatility of the equity premium, although small, are significantly higher than those in comparable adjustment cost models. However, we also show that these results require a procyclical financing premium, a property that seems at odds with the data.

A new approach for estimating and testing the linear quadratic adjustment cost model under rational expectations and I(1) variables

In this paper we propose a simple method for estimating and testing the linear quadratic adjustment cost (LQAC) model in the presence of I(1) processes. We specify the LQAC model as an ‘exact’ rational expectations model and we assume that the DGP for the observable variables belongs to the class of cointegrated error correction (ECM) models. By deriving the restrictions implied by the LQAC model on the parameters of the ECM, we propose an alternative econometric technique for the LQAC model. In contrast to existing procedures, we explicitly account for situations where the cointegration rank of the ECM is greater than the number of control variables (i.e. one). The method is applied to the demand for labor in Denmark.

Dynamic factor demands for US cigarette manufacturing under rational expectations

The rational expectations approach to adjustment cost models for factor demand is used to develop a dynamic model for US cigarette manufacturing. In the present study dynamic production modelling is extended to the case of multiple outputs. This analysis is the first to address cigarette manufacturing allowing for the possible influence of quasi-fixed factors, multiple outputs and rational expectations. Short-, intermediate-, and long-run factor demands are estimated and the presence of adjustment costs tested for in US cigarette manufacturing. The results indicate that there are significant adjustment costs associated with adjusting tobacco stock but not with adjusting the capital stock. Cigarettes produced for exports appear to differ in their marginal cost of production from cigarettes produced for sale in the US market.

Dynamic factor demands for US cigarette manufacturing under rational expectations

The rational expectations approach to adjustment cost models for factor demand is used to develop a dynamic model for US cigarette manufacturing. In the present study dynamic production modelling is extended to the case of multiple outputs. This analysis is the first to address cigarette manufacturing allowing for the possible influence of quasi-fixed factors, multiple outputs and rational expectations. Short-, intermediate-, and long-run factor demands are estimated and the presence of adjustment costs tested for in US cigarette manufacturing. The results indicate that there are significant adjustment costs associated with adjusting tobacco stock but not with adjusting the capital stock. Cigarettes produced for exports appear to differ in their marginal cost of production from cigarettes produced for sale in the US market.

Investment and uncertainty in a quadratic adjustment cost model: evidence from Brazil

This paper assesses empirically the sign of the uncertainty-investment relation in Brazil within a quadratic adjustment cost model. It is shown that these variables are negatively related in the Brazilian economy. The implication is that investment can be enlarged with the adoption of a sustainable macroeconomic policy that rules out uncertainty-yielding shocks, such as a huge devaluation in domestic currency, or defaults in internal and external debts. The paper also proposes a method for estimating the quadratic adjustment cost model when the endogenous variable is I(2) and the forcing variables are I(1). Since capital stock is typically an I(2) variable, the econometric insight seems particularly suited for models of investment.

Persistence of Capacity Shortage and the Role of Adjustment Costs

This paper finds that plant capital constraints on output in UK industry tend to persist for surprisingly long periods, reflecting a slow response of capital investment. The paper examines the conventional view that this response pattern may be explained by cost of adjustment. Using UK time‐series data for a small number of industry groups, it is shown that the observed dynamics of capital constraints (capital shortage) are not fully explained by a quadratic adjustment cost model or by alternative forms of adjustment cost.

Loss function‐based evaluation of DSGE models

AbstractIn this paper we propose a Bayesian econometric procedure for the evaluation and comparison of DSGE models. Unlike in many previous econometric approaches we explicitly take into account the possibility that the DSGE models are misspecified and introduce a reference model to complete the model space. Three loss functions are proposed to assess the discrepancy between DSGE model predictions and an overall posterior distribution of population characteristics that the researcher is trying to match. The evaluation procedure is applied to the comparison of a standard cash‐in‐advance (CIA) and a portfolio adjustment cost (PAC) model. We find that the CIA model has higher posterior probability than the PAC model and achieves a better in‐sample time series fit. Both models overpredict the magnitude of the negative correlation between output growth and inflation. However, unlike the PAC model, the CIA model is not able to generate a positive real effect of money growth shocks on aggregate output. Overall, the impulse response dynamics of the PAC model resemble the posterior mean impulse response functions more closely than the responses of the CIA model. Copyright © 2000 John Wiley & Sons, Ltd.

Measures of Fit for Rational Expectations Models: A Survey

This survey provides a detailed description of some of the recent theoretical and empirical literature on rational expectations econometrics. The survey pays special attention to non-stationarity of the data, and to the various methods for evaluating rational expectations models that have been developed as alternatives to the classical statistical approach of testing overidentifying restrictions. These methods have become very popular and widely used in empirical research. We provide an illustration using Danish stock market data, and we summarize the many results obtained recently using these measures in areas as diverse as stock prices, the term structure of interest rates, exchange rates, consumption and saving, the balance of payments, tax-smoothing, hyperinflation, and linear quadratic adjustment cost models for inventories, labour demand, and money demand.

Exchange Rate Shocks and the Speed of Trade Price Adjustment

1. Introduction Theoretical and empirical work in the international trade literature dealing with the relationship between exchange rate and trade prices has been dominated and guided by the static pass-through and profit markup model' (see, e.g., Feinberg 1986; Mann 1986; Fisher 1989; Hooper and Mann 1989; Knetter 1989; Gagnon and Knetter 1995; Feenstra, Gagnon, and Knetter 1996; and Lee 1997). The shortcoming of such models is well captured by William Branson (1989, p. 333): Difference in adjustment response signals to me the need for a reconsideration of the theoretical framework for the analysis of the pass-through question. By now, we should be thinking about optimizing price policy for investors and exporters who know that they face an exchange rate that follows some sort of stochastic process over time. These differences call for a revision of pass-through theory along the lines of time series analysis. Our explicit incorporation of profit-maximizing firms facing adjustment costs develops the model introduced by Krugman ( 1987). It transforms the traditional markup and pass-through model to explain from first principles a dynamic markup and a price adjustment speed, both depending on fundamental characteristics of the firms involved. Krugman (1989) concludes his paper on pricing to market by calling for further research on the adjustment cost model. Regarding the adjustment cost approach, he states (Krugman 1989, p. 44), It is still a speculative idea, not grounded in solid empirical tests; but it is a good story, and if it is correct, it has extremely important implications for economic policy. The present paper provides the quantity adjustment cost approach that Krugman calls for. As such, it complements the work of Gagnon (1989) and Kasa (1992). While Gagnon and Kasa employ quantity adjustment cost models with many of the same features as the model developed here, they provide only approximate solutions and focus on a quite different set of issues. Gagnon examines the effect of exchange rate variability on trade volume. Kasa investigates the importance of mean reversion in exchange rates as an explanation for the pricing to market hypothesis. In contrast, our focus is on the relation between adjustment speeds and pass-through. Thus, our contribution relative to Gagnon (1989) and Kasa (1992) is that we provide the passthrough issue in a dynamic context with exact analytical solutions that relate the degree of passthrough to adjustment speeds and identify the determinants of commodity-specific adjustment speeds in response to exchange rate shocks. The remainder of the paper is organized as follows. In section 2 we develop a partial equilibrium model, taking exchange rates as given, of the pricing policies of a profit-maximizing firm competing in foreign markets and subject to a convex quantity adjustment cost. Section 3 develops testable implications directly from the model. Section 4 discusses the data and empirical methodology for preliminary two-stage time-series and cross-sectional tests. Section 5 provides the tentative estimation, and section 6 concludes. 2. A Simple Partial Equilibrium Model Consider a representative firm producing fox export that maximizes the expected discounted value of infinite horizon real profits. The firm generates its revenue abroad in foreign currency. It has no influence on the exchange rate, may adjust its price at any point in time, but is subject to a convex cost of quantity adjustment. The firm maximizes where x is the exogenously given real exchange rate at time t. We define x as the units of domestic currency per unit of foreign currency multiplied by the export destination country's price index and divided by the home country's price index. Instantaneous profits are discounted at a rate r, which is specific to the firm; this rate accounts for a standard risk premium inherent in the riskiness of the firm's activities. …

Exchange Rate Shocks and the Speed of Trade Price Adjustment

A quantity adjustment cost model is developed in the context of international trade along the lines proposed by Krugman (1987). The model implies that prices adjust dynamically to exchange rate fluctuations. The price adjustment speed is determined as a function of foreign demand responsiveness, the appropriate discount rate, and an adjustment cost parameter. Pass‐through is incomplete and increases over time and with the speed of price adjustment. A preliminary empirical analysis finds that the speed of price adjustment from the time series by industry and then in a cross‐sectional regression tentatively relates the obtained adjustment speeds to their theoretical determinants.

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.