Score tests for zero covariances in recursive linear models for grouped or censored data

The score test statistic for testing whether an error covariance is zero is derived for a normal linear recursive model for fully observed, censored or grouped data. The test, which is obtained by regarding non-zero error covariances as arising from correlated random parameter variation, is shown to be closely related to the Information Matrix test. It turns out that the statistic, which is asymptotically N[0,1] under the null, examines the sample covariance of appropriately defined residuals.     

UK term structure decompositions at the zero lower bound

This paper employs a zero lower bound (ZLB) consistent shadow‐rate model to decompose UK nominal yields into expectation and term premium components. Compared to a standard affine term structure model, it performs relatively better in a ZLB setting by capturing the stylized facts of the yield curve. The ZLB model is then exploited to estimate inflation expectations and risk premiums. This entails jointly pricing and decomposing nominal and real UK yields. We find evidence that medium‐ and long‐term inflation expectations are contained within narrower bounds since the early 1990s, suggesting monetary policy credibility improved after the introduction of inflation targeting.     

Optimal discretionary monetary policy in a micro-founded model with a zero lower bound on nominal interest rate

This paper investigates optimal discretionary monetary policy under the zero lower bound on the nominal interest rate (ZLB) in the case of a distorted steady state due to monopoly and taxation. Solving a fully nonlinear micro-founded (FNL) model using a global method, I find that the central bank in a more distorted economy would cut the interest rate less aggressively under a particularly adverse demand shock. This occurs because inflation and nominal interest rates are higher on average, making the ZLB less likely to bind and causing the economy to escape from the ZLB sooner. However, the social planner would choose the optimal inflation rate of approximately zero. The result emerges because the unconditional benefit of avoiding the ZLB is not big enough to offset the cost of higher relative price dispersion when inflation is significantly positive. In addition, I show that the conventional linear-quadratic (LQ) method is inaccurate in the case of a sufficiently distorted steady state.     

A comparison of several approximations to the power function of the likelihood ratio test in covariance structure analysis*

In this paper we compare alternative asymptotic approximations to the power of the likelihood ratio test used in covariance structure analysis for testing the fit of a model. Alternative expressions for the noncentrality parameter (ncp) lead to different approximations to the power function. It appears that for alternative covariance matrices close to the null hypothesis, the alternative ncp's lead to similar values, while for alternative covariance matrices far from H_o the different expressions for the ncp can conflict substantively. Monte Carlo evidence shows that the ncp proposed in Satorra and Saris (1985) gives the most accurate power approximations.     

Dealing with a liquidity trap when government debt matters: Optimal time-consistent monetary and fiscal policy

How does the need to preserve government debt sustainability affect the optimal monetary and fiscal policy response to a liquidity trap? To provide an answer, we employ a small stochastic New Keynesian model with a zero bound on nominal interest rates and characterize optimal time-consistent stabilization policies. We focus on two policy tools, the short-term nominal interest rate and debt-financed government spending. The optimal policy response to a liquidity trap critically depends on the prevailing debt burden. While the optimal amount of government spending is decreasing in the level of outstanding government debt, future monetary policy is becoming more accommodative, triggering a change in private sector expectations that helps to dampen the fall in output and inflation at the outset of the liquidity trap.     

A general test for time dependence in parameters

A new test for time‐dependent parameters is proposed. The Trig‐test is based on a trigonometric expansion to approximate the unknown functional form of the variation in the parameters concerned. It is shown to have the correct empirical size and excellent power to detect structural breaks and stochastic parameter variation. The appropriate use of the Trig‐test is demonstrated by testing for structural breaks in the US inflation rate. The test detects a statistically significant increase in the US inflation rate beginning in the early 1970s and lasting through to the early 1980s. Copyright © 2004 John Wiley & Sons, Ltd.     

The implications of inflation in an estimated new Keynesian model

This paper studies the steady state and dynamic consequences of inflation in an estimated dynamic stochastic general equilibrium model of the U.S. economy. It is found that 10 percentage points of inflation entail a steady state welfare cost as high as 13% of annual consumption. This large cost is mainly driven by staggered price contracts and price indexation. The transition from high to low inflation inflicts a welfare loss equivalent to 0.53% of annual consumption. The role of nominal/real frictions as well as that of parameter uncertainty is also addressed.     

Monetary Policy and the Zero Bound to Interest Rates: A Review1

Abstract.  This paper reviews the literature on what the zero bound to nominal interest rates implies for the conduct of monetary policy. The aim is to evaluate the risks of hitting the zero bound; and to evaluate policies that are said to be able to reduce that risk, or policies that are proposed as means of helping the economy escape if it is in a zero bound 'trap'. I conclude that policies aimed at 'cure' are arguably more uncertain tools than those aimed at 'prevention', so prevention is a less risky strategy for policymakers. But since the risks of hitting the zero bound seem quite small anyway, and the risks of encountering a deflationary spiral smaller still, it is conceivable that inflation objectives that typify modern monetary regimes already have more than enough insurance built into them to deal with the zero bound problem.     

The expected real yield and inflation components of the nominal yield curve

The term structure of real yields and expected inflation are two unobserved components of the nominal yield curve. The primary objectives of this study are to decompose nominal yields into their expected real yield and inflation components and to examine their behaviour using state-space and regime-switching frameworks. The dynamic yield-curve models capture three well-known latent factors – level, slope, and curvature – that accurately aggregate the information for the nominal yields and the expected real and inflation components for all maturities. The nominal yield curve is found to increase slightly with a slope of about 120 basis points, while the real yield curve slopes upward by about 20 basis points, and the expected inflation curve is virtually flat at slightly above 2 per cent. The regime-switching estimations reveal that the nominal yield, real yield and expected inflation curves have shifted down significantly since 1999.     

Real and nominal wage rigidities in collective bargaining agreements

An earlier study of wage agreements, reached in the Canadian unionized sector between 1976–99, found that wage adjustment is characterized by downward nominal rigidity and significant spikes at zero. We extend this earlier approach to encompass the possibility of real as well as nominal wage rigidity. The addition of real wage rigidity variables enhances earlier results and suggests that real rigidity increases significantly the mass in the histogram bin containing the mean anticipated rate of inflation, as well as in adjacent bins. Downward nominal wage rigidities and spikes at zero remain important.     

A note on studentizing a test for heteroscedasticity

Breusch and Pagan (1979) have recently proposed a convenient test for heteroscedasticity in general linear models. This note derives the asymptotic distribution of their test under sequences of contiguous alternatives to the null hypothesis of homoscedasticity. The test is shown to possess asymptotically incorrect size (nominal significance level) except in the case of strictly Gaussian disturbances. A slight modification of the test is proposed which corrects this defect.     

Some tests for the constancy of regressions under heteroscedasticity

For testing the equality of coefficients of a linear regression model under heteroscedasticity, we suggest an F criterion conditioned on the posterior mean of the ratio of standard deviations of error terms in two subsamples. For pairable subsamples, and exact F test is derived. Sampling experiments show that the Chow test differs substantially from the nominal significance level when the two subsample sizes are unequal, and that the F test conditioned on the posterior mean is superior to other tests when sample sizes are small.     

The long-run implications of the production smoothing model of inventories: An empirical test

This paper provides an empirical test of the long-run implications of the production smoothing model of inventories, the dominant framework for inventory investment research in the past. Intertemporal models of a firm holding inventories of finished goods predict a long-run relationship between inventories, shipments, factor input prices, and the real interest rate which is tested here using cointegration test procedures. These tests provide little support for the predictions of the production smoothing model. In most of the data sets used, test statistics indicate that inventories, shipments, factor input prices, the nominal interest rate, and the inflation rate maintain a long-run equilibrium relationship but parameter estimates of cointegrating vectors are often implausible, typically rejecting hypotheses implied by structural models of the production smoothing motive for holding inventories.     

Yield curve in an estimated nonlinear macro model

This paper estimates a sticky price macro model with US macro and term structure data using Bayesian methods. The model is solved by a nonlinear method. The posterior distribution of the parameters in the model is found to be bi-modal. The degree of nominal rigidity is high at one mode (“sticky price mode”) but is low at the other mode (“flexible price mode”). I find that the degree of nominal rigidity is important for identifying macro shocks that affect the yield curve. When prices are more flexible, a slowly varying inflation target of the central bank is the main driver of the overall level of the yield curve by changing long-run inflation expectations. In contrast, when prices are more sticky, a highly persistent markup shock is the main driver. The posterior probability of each mode is sensitive to the use of observed proxies for inflation expectations. Ignoring additional information from survey data on inflation expectations significantly reduces the posterior probability of the flexible price mode. Incorporating this additional information suggests that yield curve fluctuations can be better understood by focusing on the flexible price mode. Considering nonlinearities of the model solution also increases the posterior probability of the flexible price mode, although to a lesser degree than using survey data information.     

Testing for autoregressive against moving average errors in the linear regression model

This paper presents a new approach to hypotheses testing problems which are non-nested in the classical sense and which concern the covariance matrix of the disturbance vector of the linear regression model. In particular, the application of the approach to testing for AR(1) disturbances against MA(1) disturbances is explored in some detail. Practical difficulties are discussed and selected upper bounds for the test's five percent significance points are tabulated. The small sample power of four versions of the new test are compared empirically and a clear conclusion is made in regard to the best overall test.     

Tests of non-nested regression models: Small sample adjustments and Monte Carlo evidence

It is known that the small sample significance levels of Cox-type tests of non-nested regression models can be much greater than the nominal level. Adjustments designed to overcome this problem are discussed and two tests are proposed. Monte Carlo evidence on the performance of the tests derived in this paper, the Davidson-MacKinnon J-test and the Fisher-McAleer test is presented. The F-test applied to the comprehensive model is also included in the simulation experiments.     

Nonlinear dynamics of interest rate and inflation

According to several empirical studies US inflation and nominal interest rates as well as the real interest rate can be described as unit root processes. These results imply that nominal interest rates and expected inflation do not move one‐for‐one in the long run, which is incongruent with theoretical models. In this paper we introduce a new nonlinear bivariate mixture autoregressive model that seems to fit quarterly US data (1953 : II–2004 : IV) reasonably well. It is found that the three‐month Treasury bill rate and inflation share a common nonlinear component that explains a large part of their persistence. The real interest rate is devoid of this component, indicating one‐for‐one movement of the nominal interest rate and inflation in the long run and, hence, stationarity of the real interest rate. Copyright © 2006 John Wiley & Sons, Ltd.     

Indexed versus nominal government debt under inflation and price-level targeting

This paper presents a DSGE model in which long run inflation risk matters for social welfare. Optimal indexation of long-term government debt is studied under two monetary policy regimes: inflation targeting (IT) and price-level targeting (PT). Under IT, full indexation is optimal because long run inflation risk is substantial due to base-level drift, making indexed bonds a better store of value than nominal bonds. Under PT, where long run inflation risk is largely eliminated, optimal indexation is substantially lower because nominal bonds become a relatively better store of value. These results are robust to the PT target horizon, imperfect credibility of PT and model calibration, but the assumption that indexation is lagged is crucial. A key finding from a policy perspective is that indexation has implications for welfare comparisons of IT and PT.     

Relative Efficiency of the Fuzzy p-Value Approach to Hypothesis Testing

In missing data problems, it is often the case that there is a natural test statistic for testing a statistical hypothesis had all the data been observed. A fuzzy  p -value approach to hypothesis testing has recently been proposed which is implemented by imputing the missing values in the "complete data" test statistic by values simulated from the conditional null distribution given the observed data. We argue that imputing data in this way will inevitably lead to loss in power. For the case of scalar parameter, we show that the asymptotic efficiency of the score test based on the imputed "complete data" relative to the score test based on the observed data is given by the ratio of the observed data information to the complete data information. Three examples involving probit regression, normal random effects model, and unidentified paired data are used for illustration. For testing linkage disequilibrium based on pooled genotype data, simulation results show that the imputed Neyman Pearson and Fisher exact tests are less powerful than a Wald-type test based on the observed data maximum likelihood estimator. In conclusion, we caution against the routine use of the fuzzy  p -value approach in latent variable or missing data problems and suggest some viable alternatives.     

Combining competing forecasts of inflation using a bivariate arch model

This paper sets out the basic structure of the bivariate generalization of Engle's ARCH model. Conditions which guarantee that the conditional covariance matrix is well defined are summarized, as are estimation and hypothesis testing.The process is used to combine forecasts where the weights are allowed to vary over time. Forecast errors from competing models are treated as a bivariate ARCH process so that the conditional covariance matrix adapts over time. At each point in time these conditional estimates of the variances and covariances are used to construct the optimal weights for combining the forecasts. Consequently, when one model is fitting well, its variance will be reduced and its weight will be increased.Two models of US inflation are constructed; one is a stylized monetarist model while the other is a mark-up model. The forecast errors are modeled as a simple bivariate ARCH process. Diagnostic tests reveal that this has overly restricted the parameterization of the covariance matrix. An approximation to the theoretically anticipated factor structure model is then estimated. The results in both cases show the weights varying over the sample period in moderately interpretable fashion.