Andy Snell

TESTING FOR COINTEGRATION IN NONLINEAR SMOOTH TRANSITION ERROR CORRECTION MODELS

This paper proposes a new testing procedure to detect the presence of a cointegrating relationship that follows a globally stationary smooth transition process. In the context of nonlinear smooth transition error correction models (ECMs) we provide two simple operational versions of the tests. First, we obtain the associated nonlinear ECM-based tests. Second, we derive the nonlinear analogue of the residual-based test for cointegration in linear models. We derive the asymptotic distributions of the proposed tests. Monte Carlo simulation exercises confirm that our proposed tests have much better power than the linear counterparts against the alternative of a globally stationary nonlinear cointegrating process. In an application to the price-dividend relationship, our test is able to find cointegration, whereas the linear-based tests fail to do so.We are grateful to an associate editor, two anonymous referees, Richard Baillie, In Choi, Atanas Christev, Hira Koul, Richard Harris, Cheng Hsiao, Changjin Kim, Joon Park, Peter Schmidt, Yoonjae Whang, Jeff Wooldridge, and seminar participants at University of Edinburgh, Heriot-Watt University, Korea University, University of Leeds, Michigan State University, University of Newcastle, and Sungkunkwan University for their helpful comments. Partial financial support from the ESRC (grant R000223399) is gratefully acknowledged. The usual disclaimer applies.

Temporal aggregation and the power of tests for a unit root

Abstract The asymptotic local power of unit root tests with the same data span is shown to be independent of sampling frequency. A measure of the power trade-off between sampling frequency and time span for distinct alternatives is derived using an approximate slopes approach. Only small span increases are generally required to maintain power when reducing sampling frequency. Monte Carlo results support the asymptotic analysis for finite samples. An application is made to a consumption function for the UK. Cointegration of consumption and wealth is rejected with quarterly data but convincingly accepted with a longer span of annual data.

Testing for Cointegration in Nonlinear STAR Error Correction Models

In this paper we propose a new testing procedure to detect the presence of a cointegrating relationship that follows a globally stationary smooth transition autoregressive (STAR) process. We start from a general VAR model, embed the STAR error correction mechanism (ECM) and then derive the generalised nonlinear STAR error correction model. We provide two operational versions of the tests. Firstly, we obtain the associated nonlinear ECM-based test. Secondly, we generalise the well-known residual-based test for cointegration in linear models by Engle and Granger (1987) and obtain its nonlinear analogue. We derive the relevant asymptotic distributions of the proposed tests. We find via Monte Carlo simulation exercises that our proposed tests have much better power than the Engle and Granger test against the alternative of a globally stationary STAR cointegrating process. In an application to the price-dividend relationship, we also find that our test is able to find cointegration, whereas the linear-based tests fail to do so. Further analysis of impulse response functions of error correction terms (under the alternative) shows that the time taken to recover one half of a one standard deviation shock varies between five and twenty years, whereas the time taken to recover one half of a large shock varies between just 4 to 18 months. This clearly implies that data periods dominated by extreme volatility may display substantial mean reversion of the price-dividend relationship. By contrast this relationship may well look like a unit root when the underlying shocks take on smaller values.

Mean Group Tests for Stationarity in Heterogeneous Panels

This paper proposes the panel-based mean group tests for the null of stationarity against the alternative of unit roots in the presence of both heterogeneity across cross-section units and serial correlation across time periods. Using both sequential and joint asymptotic analyses the proposed test statistic is shown to be distributed as standard normal under the null for large N (number of groups) and large T (number of time periods). Monte Carlo results support the use of join asymptotic limits (under further condition that N/T -> 0) as a guide to finite sample performance, but also clearly indicate that the power of our suggested panel-based test is substantially higher than that of the single time series-based test.

Downward Wage Rigidity in a Model of Equal Treatment Contracting

Following insights by Bewley (1999a), this paper analyses a model with downward rigidities in which firms cannot pay discriminately based on year of entry to the firm, and develops an equilibrium model of wages and unemployment. We solve for the dynamics of wages and unemployment under conditions of downward wage rigidity, where forward-looking firms take into account these constraints. We show that there is a frontloading incentive that leads to a simple solution in the case of certainty. Using productivity data from the postwar US economy, we analyse the ability of the model to match certain stylised labour market facts.

The sweet taste of information: a study of the demand for new brands in the UK confectionery industry

This paper tests the hypothesis derived in Tonks (1986) that the demand for a product becomes more elastic over time. In the early periods of a products life the demand curve is relatively inelastic as consumers purchase the good to learn about its unknown qualities. Over time as information accumulates, consumers become more price-conscious. The study makes use of data on eight products in the UK confectionery industry produced by Rowntree Mackintosh PLC, introduced onto the market over the period 1976–81. The study tests the hypothesis in two ways: first it applies a standard demand curve to two subperiods, to test for parameter stability; secondly it incorporates an information variable to take account of the full-information demands in the later periods. Both tests provide tentative support for the hypothesis.

Bias in Returns to Tenure When Firm Wages and Employment Comove: A Quantitative Assessment and Solution

It is well known that unless worker-firm match quality is controlled for, reduced-form estimates of returns to firm tenure will be biased. In this paper, we show that there is a further pervasive source of bias, namely, the comovement of firm employment and firm wages. We argue that firm-year fixed effects must be used to eliminate this bias. Estimates from two large-panel data sets from Germany and Portugal show that the bias is empirically important. Finally, we show that the results extend to tenure correlates used in macroeconomics, such as the minimum unemployment rate since joining the firm.

A Competitive Model of Worker Replacement and Wage Rigidity

We adapt the models of Menzio and Moen (2010) and Snell and Thomas (2010) to consider a labour market in which firms can commit to wage contracts but cannot commit not to replace incumbent workers. Workers are risk averse, so that there exists an incentive for firms to smooth wages. Real wages respond in a highly non-linear manner to shocks, exhibiting downward rigidity, and magnifying the response of unemployment to negative shocks. We also consider layoffs and show that for a range of shocks labor hoarding occurs while wages are cut. We argue these features are consistent with recent evidence.