The instantaneous speed of adjustment assumption and stability of economic models

Summary In order to simplify stability analysis of an economic model one can assume that one of the model variables moves infinitely fast towards equilibrium, given the values of the other slower variables. We present conditions such that stability of the simplified model implies, or is implied by, stability of the original model. The conditions make use of the concept of a negative dominant diagonal. As an example, we analyse the (local) stability of a Walrasian general equilibrium model.Useful comments on an earlier version of this paper by an anonymous referee are gratefully acknowledged.     

A note on estimating disequilibrium models with aggregation

When an aggregate disequilibrium is the result of disequilibrium in several submarkets, the usual maximum likelihood estimation, which is based on the min of aggregate demand and supply, represents a misspecification. The present paper compares ML with several nonlinear least squares methods that are appropriate for this situation. Monte Carlo experiments suggest that ML is robust with respect to the misspecification and may be preferable to the nonlinear least suqares methods in some situations.     

The speed of adjustment of the actual to the desired money stock: A comparative study

This article examines whether there are significant differences in the speed of adjustment of the actual to the desired money stock among major industrialized countries. Demand for money functions, including a partial adjustment hypothesis, were estimated for the United States, United Kingdom, Canada, Germany, France and Japan essentially over the period 1960–1976. The functions were tested for stability and found to be stable in most cases. The estimations show that, mainly with the exception of Germany and the United Kingdom for broad money, the speed of adjustment is relatively high. These results tend to support monetarist views. The statistical test for differences in the speed of adjustment revealed that only a few significant differences exist when narrow money is used. When broad money is used, howeever, the United Kingdom and Germany are shown to have significantly slower speeds of adjustment than almost all the other countries.     

A note on implicit inventory behavior in cyclical macroeconomic models with excess demand

The paper is concerned with dynamic models that allow for non-zero excess demand on goods markets but abstain from considering possible feedback effects of stock-piling. That is, inventories are only implicitly determined. Consistency requires that they do not fall below zero and, relative to output, do not grow beyond all bounds. With respect to periodic motions, conditions for consistency as well as for inconsistency are derived. It is indicated that a priori, in particular in the presence of long-run growth, inconsistency may not be an exception.     

Scale economies with regard to price adjustment costs and the speed of price adjustment in Australian manufacturing

This paper aims to examine the impact of firm size, industry concentration and the length of production on industry speed of price adjustment. To motivate the paper, an industry pricing model in error correction form is derived from firm pricing behaviour. As a new development, firms are assumed to have price adjustment costs that are a function of their size. The empirical model is estimated using two‐digit Australian manufacturing industry data for the period 1994:3 to 2006:1. The results suggest that the industry speed of price adjustment is positively related to firm size and negatively related to industry concentration and the production lag. Implied values for industry speeds of price adjustment are generally small when compared to other country industry studies. However, the industry average median lag of 7.1 quarters indicates a slightly faster speed of price adjustment than the estimate for the Australian consumer price index by Dwyer and Leong (2001 Dwyer, J. and Leong, K. 2001. Changes in the determination of inflation in Australia 1–44. Reserve Bank of Australia Research Discussion Paper 2001‐02 [Google Scholar]).     

Regional variation in the capital structure adjustment speed of listed firms: Evidence from China

This paper investigates whether in China, a country large in size, geographically diverse and imbalanced in regional economic development, variation in firm capital structure¹ is systematically related to regional economic environment. In addition, we examine whether during macroeconomic recovery there is significant difference in the speed of adjustment in capital structure of firms located in different regions. The empirical analyses are based on 783 firms listed on Shanghai and Shenzhen Stock Exchanges during a sample period of year 2000 through 2014. Using GMM and Logit QMLE, we found strong evidence that the regional variation in the capital structure of listed firms is linked to growth indicator (the Market-to-Book value, MB), EBIT ratio, size of the firm and tangible assets (the value of Net Property, Plant and Equipment, PPE). In the process of economic recovery, there was apparent regional variation in the speed of adjustment in capital structure, i.e. the fastest adjustment in capital structure was found in East China while that of West China followed and that of Mid China the slowest, that is to say within a given period the leverage ratio of listed firms in East China rises or falls faster than in the other two regions.     

The use of ARIMA models in seasonal adjustment

This paper compares the traditional Census X-11 method for seasonal adjustment with two recent alternative methods using ARIMA models, viz. X-11 ARIMA and Burman's signal extraction method. No strong preference results for one of these methods when applied to a number of macro-economic time series for the Netherlands.     

On the use and misuse of the instantaneous speed of adjustment assumption

A commonly used simplifying assumption in dynamics is that one of the variables moves infinitely fast to its equilibrium value, given the current values of the slower variables. If a theorist believes that one of his variables is fast relative to the others, how safe is he in setting the system up as if the relatively fast variable were infinitely fast? How do the dynamics of the simplified system compare with those of the true system? In this paper, the notion of adjustment speed is analysed and a new definition is offered. It is found that the simplified system behaves like the true system only in highly unlikely cases.     

Aggregation in models with quantity constraints: The CES aggregation function

This paper is devoted to the problem of aggregation in models with quantity constraints. The focus is on quantity rationing macroeconomic (QRM) models where the micromarket outcome can be written as the minimum of several variables and where the diversity of situations across micromarkets is explicitly recognized. The aggregation result given in this paper generalizes that of Lambert (1988) to employment functions with more than two components, and leads to approximate aggregate functions of the CES variety. The approximation used can accomodate general variance-covariance structures. Simulation experiments show that the approximation error remains within reasonable bounds (1–4%). It thus seems that the CES formulation can accomodate a large variety of situations. It remains in particular valid when the (restrictive) conditions required to obtain the CES function as an exact result (independently and identically distributed Weibull variables) are not satisfied. First version received: July 1997/Final version received: March 1999     

From small to large: A systematic comparison of gradually more complex econometric models

This paper treats the problem of validating macroeconometric models. A set of nine models are estimated on the same data base and subjected to the same simulation tests. They range from the simple IS model to a relatively realistic model of the Swedish economy in the postwar period. The main conclusion is that minor specification changes may drastically alter the dynamic characteristics of models, despite the fact that the models are theoretically plausible. A second purpose of the paper is to try to bridge the gap between the simple IS or IS-LM models used in the classroom and the much larger and more complex models that are actually used.     

Less than perfect aggregation of input-output models: The choice of bounds

An upper bound used in consolidating input-output models is shown to be non-minimal, and thus non-optimal. The least upper bound is then obtained. Non-least upper bounds are shown to be useful only when complemented by corresponding lower ones.     

Separability and capital aggregation in sectoral models of US production

Separability plays a fundamental role in applied studies of production inasmuch as it provides for consistent aggregation and allows multi-stage estimation of models with many inputs. This paper examines whether two types of capital, structures and equipment, are weakly separable from labour and energy and materials in sectoral models of US production, and provides an assessment of the effects of maintaining capital separability. The study focuses on the elasticity of substitution as a measure of input association and associated standard errors and confidence intervals based on bootstrapping. Elasticity estimates and tests indicate that capital separability is generally inconsistent with data representing sectoral US production. Elasticity sign, however, appears robust to capital aggregation and performs especially well as an indicator of input association.     

Estimating the speed of adjustment of European banking efficiency under a quadratic loss function

This paper investigates the speed of adjustment of cost efficiency to equilibrium level in the European banking industry. Our analysis provides for the first time insights into the process of convergence across European banking markets as measured by the speed of adjustment of cost efficiency. In particular, we employ a quadratic loss function specification based on forward-looking rational expectations to model the underlying dynamics of efficiency scores in the banking industry of the EU-15 region over the period 1998–2005. Results show that there is considerable variation in the speed of adjustment across banking systems, while over time it appears that continuing efforts to advance financial integration have led to some improvement in the speed of adjustment to the long-run equilibrium.     

Increasing returns and unsynchronized wage adjustment in sunspot models of the business cycle

A challenge to models of equilibrium indeterminacy based on increasing returns is that required increasing returns for generating indeterminacy can be implausibly large and rise quickly with the relative risk aversion in labor. We show that unsynchronized wage adjustment via a relative wage effect can both lower the required degree of increasing returns for indeterminacy to a plausible level and make it invariant to the relative risk aversion in labor. Consequently, indeterminacy and sunspot-driven fluctuations can emerge for plausible increasing returns regardless of the relative risk aversion in labor. Our model generates reasonable dynamics in terms of matching the business cycle, and sunspot shocks become more important with labor market friction.     

Reducing unwanted consequences of aggregation in large-scale economic models - A systematic empirical evaluation with the GTAP model

We discuss how to avoid aggregation bias in large-scale global Computable General Equilibrium (CGE) models by reducing the need of pre-model aggregation, based on the combination of algorithmic improvements and a filtering approach which removes small transactions. Using large-scale sensitivity analysis, we show the impact of pre-aggregation and filtering on model size, model solution time and simulated welfare impacts, using a multi-lateral partial trade liberalization simulated with the standard GTAP model as the test case. We conclude that pre-model aggregation should be avoided as far as possible, and that our filtering approach and algorithmic improvements allow global CGE analysis even with highly disaggregated data sets at moderate solution times.     

Large data sets,nonlinearity and the speed of adjustment to real exchange rate shocks

A well known puzzle in international finance concerns the very slow speeds of adjustment of real exchange rates observed in response to shocks. In this article, we explore whether allowing for a wide range of influences on the real exchange rate in a nonlinear framework can help resolve this puzzle. Using, recently proposed econometric methods for summarizing very large macroeconomic data sets into a small number of observable factors, we find that there is a long run relationship between these factors and real exchange rates. When put into a nonlinear framework, we find that allowing for the effects of macroeconomic factors dramatically increases the measured speed of adjustment of the real exchange rate.     

Non-convexities in the adjustment of different capital inputs: A firm-level investigation

Recent developments in investment research have highlighted the importance of non-convexities and irreversibilities in firms’ adjustment of quasi-fixed inputs. Aggregation across capital goods may smooth out the discontinuities associated with the adjustment of individual assets. Lack of suitable data is one of the reasons why empirical work has typically relied on the assumption of capital homogeneity. In this paper we exploit a data set of 1539 Italian firms which allows us to disaggregate capital into equipment and structures, and purchases and sales of assets. We construct measures of fundamental Q to capture investment opportunities associated with each asset. We uncover the pattern of dynamic adjustment by using non-parametric techniques to relate each individual investment to its own fundamental Q.