Long-run Parameters Research Articles

UK Business Investment: Long-Run Elasticities and Short-Run Dynamics

Theory tells us that output, the capital stock and the user cost of capital are related. From the capital accumulation identity, it also follows that the capital stock and investment have a long-run proportional relationship. The dynamic structure thus implies a multi-cointegrating framework, in which separate cointegrating relationships are identifiable. This has been used to justify the estimation of investment equations embodying a reduced-form long-run relationship between investment and output (rather than between the capital stock and output). In this paper, a new investment equation is estimated in the full structural framework, exploiting a measure of the capital stock constructed by the Bank, and a long series for the cost of capital. A CES production function is assumed, and a well-determined estimate of the elasticity of substitution is obtained by a variety of measures. The robust result is that the elasticity of substitution is significantly different from unity (the Cobb-Douglas case), at about 0.45. Overidentifying restrictions on the long-run relationship are all accepted. Although the key long-run parameter (the elasticity of substitution) is highly robust to alternative specifications, single-equation investment relationships may obscure the dynamics. There is evidence that the Johansen method is oversized, but given this, a test for excluding the capital accumulation identity from the investment equation is much better than using a single-equation ECM.

A new interpretation of the exchange rate–yield differential nexus

AbstractEmpirical studies have had difficulty in establishing the long‐run relationship between real exchange rates and real yield differentials predicted by sticky price exchange rate models. We revisit this issue in a nonstationary panel regression framework. This facilitates estimation of a long‐run parameter even when the underlying relation‐ship is subject to permanent shocks or the variables do not cointegrate. The slope coefficient estimate from a sample of 23 industrialized countries 1973M1–1998M12 has the correct sign and is statistically significant for both short and long‐term yields. These results support fundamentals‐based models of exchange rate behaviour while permitting real factors to play a role. Moreover, they indicate that capital markets integration is more advanced than hitherto believed. Copyright © 2004 John Wiley & Sons, Ltd.

Aggregate Loans to the Euro Area Private Sector

This paper provides new evidence on the behaviour of euro area aggregate loans to the private sector. Using a sample covering the last twenty years, a cointegrating vector linking the real stock of loans to a small set of domestic macroeconomic variables is found. Besides real GDP and prices, this set includes a new measure of the cost of loans obtained as a weighted average of bank lending rates. The results are overall encouraging, though the recursive estimates of the long-run parameters suggest that in 2000 some disturbances, probably of a temporary nature, affected the system. The study then addresses the issue of the leading indicator properties of loans. It finds that the deviations of the real stock of loans from the equilibrium level implied by the model seem to contain information on future changes in inflation, though not on its level. JEL Classification: C32, C51

Cointegration and the Monetary Exchange Rate Model Revisited*

To test for cointegration in a multiple of countries a number of procedures are available: a panel vector error correction framework, a panel-data version of the Engle and Granger (1987) two-step procedure and the Johansen (1991) trace statistic. We apply these three methods on two four-country datasets consisting of the exchange rate data and monetary fundamentals relative to both the United Kingdom and the United States to test the empirical validity of the monetary exchange rate model. Of the three aforementioned methods only the panel vector error correction approach provides evidence for the validity of both the cointegration restriction as well as the long-run parameter restrictions of the monetary model, irrespective of the numeraire country. Copyright 2002 by Blackwell Publishing Ltd

Nonlinear minimization estimators in the presence of cointegrating relations

Abstract In this paper, we consider estimation of a long-run and a short-run parameter jointly in the presence of nonlinearities. The theory developed establishes limit behavior of minimization estimators of the long- and short-run parameters jointly. Typically, if the long-run parameter that is present in a cointegrating relationship is estimated, its estimator will be superconsistent. Therefore, we may conjecture that the joint minimization estimation of both parameters jointly will result in the same limit distribution for the short-run parameter as if the long-run parameter was known. However, we show that unless a regularity condition holds, this intuition is false in general. This regularity condition, that clearly holds in the standard linear case, is identical to the condition for validity of a two-step Granger–Engle type procedure. Also, it is shown that if the cointegrated variables are measured in deviation from their averages, the standard asymptotic normality result (that one would obtain if the long-run parameter was known) holds.

LONG-RUN STRUCTURAL MODELLING

The paper develops a general framework for identification, estimation, and hypothesis testing in cointegrated systems when the cointegrating coefficients are subject to (possibly) non-linear and cross-equation restrictions, obtained from economic theory or other relevant a priori information. It provides a proof of the consistency of the quasi maximum likelihood estimators (QMLE), establishes the relative rates of convergence of the QMLE of the short-run and the long-run parameters, and derives their asymptotic distributions; thus generalizing the results already available in the literature for the linear case. The paper also develops tests of the over-identifying (possibly) non-linear restrictions on the cointegrating vectors. The estimation and hypothesis testing procedures are applied to an Almost Ideal Demand System estimated on U.K. quarterly observations. Unlike many other studies of consumer demand this application does not treat relative prices and real per capita expenditures as exogenously given.

An aggregate model for the European Union

We present the structure and properties of an aggregate model for the European Union considered as a whole. Such a model can be complementary to those consisting of an aggregation of national sub-models, and is probably superior to them in several economic policy analyses. The equations have been estimated by a two-stage procedure that takes into account the possible presence of structural breaks in the long-run parameters. The estimation of the error correction models allows for the non-linearity and simultaneity of the dynamic system. The estimation results have led to equations endowed with high fitting power, supporting the hypothesis that behavioural equations for the EU can be defined at a supranational level in a meaningful way. The validity of this aggregate approach is confirmed by several simulation experiments.

LONG-RUN STRUCTURAL MODELLING

The paper develops a general framework for identification, estimation, and hypothesis testing in cointegrated systems when the cointegrating coefficients are subject to (possibly) non-linear and cross-equation restrictions, obtained from economic theory or other relevant a priori information. It provides a proof of the consistency of the maximum likelihood (ML) estimators, establishes the relative rates of convergence of the ML estimators of the short-run and the long-run parameters, and derives their asymptotic distribution; thus generalizing the results already available in the literature for the linear case. The paper also develops tests of the over-identifying (possibly) non-linear restrictions on the cointegrating vectors. The estimation and hypothesis testing procedures are applied to an Almost Ideal Demand System estimated on U.K. quarterly observations. Unlike many other studies of consumer demand this application does not treat relative prices and real per capita expenditures as exogenously given.

An Aggregate Model for the European Union

We present the structure and properties of an aggregate model for the European Union, consisting of 34 equations estimated on annual data aggregated over the twelve-member EU, ranging from 1960 to 1997. Estimation was performed by a two-stage procedure taking into account the possible presence of structural breaks in the long-run parameters and allowing for nonlinearity and simultaneity of the dynamic equations. The estimated equations have a very good fit and pass a number of diagnostic tests, suggesting that EU-wide behavioural equations can be defined in a meaningful way. Simulation experiments show that the model is an agile and effective tool for the study of the European economy at an aggregate level. In particular, the model is shown to improve over previous aggregate explanations of the European economy, in that its dynamic multipliers provide a better account of the European unemployment and inflation dynamics in the last decade.

Money demand in Hungary and Poland

This paper analyses the determinants and the stability of money demand functions in Hungary and Poland, using an error-correction framework. The null of stable cointegration relationships cannot be rejected in some specifications. The results suggest that long-run parameters are in line with economic theory. While judging the appropriateness of different strategies of monetary policy on the basis of these findings alone would be premature, the paper suggests that money demand functions can serve as a useful reference for monetary authorities.

Money demand in Hungary and Poland

This paper analyses the determinants and the stability of money demand functions in Hungary and Poland, using an error-correction framework. The null of stable cointegration relationships cannot be rejected in some specifications. The results suggest that long-run parameters are in line with economic theory. While judging the appropriateness of different strategies of monetary policy on the basis of these findings alone would be premature, the paper suggests that money demand functions can serve as a useful reference for monetary authorities.

Working time, employment, and work sharing: Evidence from Sweden

We study three questions which are important for work sharing to increase employment. First, is there a negative long-run relation between working time and employment? Second, are hours per worker exogenous with respect to wages and employment? Third, can policy makers influence actual hours per worker? We formulate a theoretical model for employment, hours per worker, production, and real wages. A VAR model with cointegrating constraints is estimated by maximum likelihood using Swedish private sector data 1970:1–1990:4. We find (i) no long-run relation between hours per worker and employment, (ii) that hours per worker are endogenous with respect to the estimation of long-run parameters, and (iii) that legislated working time and hours per worker are related to each other in the long run.

Employment, output and political business cycle effects in the Greek non-tradable sector

Starting from a theoretical model with traded and non-traded goods, a long-run labour demand equation is identifed, with employment being proportional to relative output and prices. Using Greek data, the model supports weak exogeneity of relative prices and fiscal expansion with respect to the long-run parameters in the cointegrating space. It also highlights structural rigidities in the functioning of the Greek labour market. Political business cycle and partisan effects are shown to affect the short-run employment decisions.

Some tests for parameter constancy in cointegrated VAR‐models

Some methods for the evaluation of parameter constancy in cointegrated vectorautoregressive (VAR) models are discussed. Two different ways of re-estimating the VAR-model are proposed; one in which all parameters are estimated recursively based upon the likelihood function for the first observations, and another in which the cointegrating relations are estimated recursively from a likelihood function, where the short-run parameters have been concentrated out. We suggest graphical procedures based on recursively estimated eigenvalues to evaluate the constancy of the long-run parameters in the model. Specifically,we look at the time paths of the eigenvalues using a new result on the asymptotic distribution of the estimated eigenvalues. Furthermore, we show that the fluctuation test by Ploberger et al. (1989) and the Lagrange multiplier (LM) type test for constancy of parameters by Nyblom (1989) can be applied to test the constancy of the long-run parameters in the cointegrated VAR-model. All results are illustrated using a model for the term structure of interest rates on US Treasury securities.

Weak exogeneity in I(2) VAR systems

This paper defines parametric conditions under which a subset of variables is weakly exogenous with respect to the (multi)-cointegration parameters in I(2) VAR systems. The weak exogeneity conditions can be interpreted in terms of common trends, corresponding to the cumulation of the errors from the marginal equations into the I(2) trends, or in terms of ‘no levels and difference feedback’ into the marginal model equations. A modified version of the two-stage procedure proposed in Johansen (1995) is adopted for conditional statistical inference. Corresponding tests for the above restrictions are derived and discussed. Asymptotic properties of the tests and of the conditional estimators are analyzed. It is shown that if the conditions of weak exogeneity do not apply, the conditional estimators of the long-run parameters can be inconsistent and/or present limit distributions with nuisance parameters, according to which part of the conditions fails to hold. A test for weak exogeneity restrictions as a routine check before any analysis of conditional models is strongly recommended.

Labor Market Decisions and Greek Manufacturing Competitiveness

Starting from a Vector Error-Correction Model (VECM), we identify a long-run labor demand equation, with employment being proportional to both value added and product wages. The system supports weak exogeneity of output and product wages with respect to the long-run parameters in the cointegrating space. It also highlights structural rigidities in the functioning of the Greek labor market. Strike activity raises employment in the short-run, while unemployment benefits have negative short-run effects.

Incidence of tariff: the case of India, 1982-93

In this paper, the effect of tariff is analysed at a broad sectoral level using a simple general equilibrium model. The sectors of the Indian economy have been classified on the basis of trade. Commodities have been identified as importables or exportables based on whether India is a major importer or exporter of a particular product. We have used an indirect approach to estimate the shift parameter employing time-series regression of changes in the relative price of non-tradeables to exportables and that of importables to exportables. The series were tested for stationarity and they were found to be stationary in the first differences. We used a dynamic specification to allow for lags in the adjustment of relative prices of non-tradeables to exportables due to changes in the relative price of importables to exportables. The estimate of the long-run shift parameter is found to be 0.74% and the estimate of the short-run shift parameter is 0.58%. Our results show that a 100% rate of customs duty results in ‘true’ protection of importable only to the extent of 14.9% in the long-run and a bias against exports to the extent of 42.5%.

COINTEGRATION AND CHANGES IN REGIME: THE JAPANESE CONSUMPTION FUNCTION

In this paper we examine a model of cointegration where long-run parameters are subject to switching between several different cointegrating regimes. These shifts are allowed to be governed by the outcome of an unobserved Markov chain with unknown transition probabilities. We illustrate this approach using Japanese data on consumption and disposable income, and find that the data favour a Markov-switching long-run relationship over a standard temporally stable formulation. © 1997 by John Wiley & Sons, Ltd.

Testing between alternative wage-employment bargaining models using Belgian aggregate data

In this paper, we discriminate among alternative models of bargaining for wages and employment (right-to-manage, efficient bargaining and general bargaining models) using Belgian aggregate data. We estimate the ECM representation of a dynamic employment equation for each model using Engle-Granger's two-step estimation procedure. We use Phillips-Hansen's FME to obtain long-run parameter estimators which are optimal and asymptotically normally distributed. On the basis of non-nested tests, both the right-to-manage and the hypothesis that wage-employment negotiations are efficient are rejected in favour of the general bargaining model where outcomes are inefficient.

A Symmetric Approach to Canadian Meat Demand Estimation

Variability in published meat demand elasticity estimates for Canada motivates examining the importance of dynamics and endogeneity of right-hand-side variables. Wickens and Breusch suggest a re-parameterization of dynamics which allows estimating the long-run parameters directly and maintains linearity. A symmetric approach, employing both ordinary and inverse demand systems, to endogeneity of right-hand-side variables is used. Endogeneity of both prices and quantities is examined. Results show both dynamics and endogeneity are important in quarterly Canadian meat demand.