A new coincident index of business cycles based on monthly and quarterly series

Popular monthly coincident indices of business cycles, e.g. the composite index and the Stock–Watson coincident index, have two shortcomings. First, they ignore information contained in quarterly indicators such as real GDP. Second, they lack economic interpretation; hence the heights of peaks and the depths of troughs depend on the choice of an index. This paper extends the Stock–Watson coincident index by applying maximum likelihood factor analysis to a mixed‐frequency series of quarterly real GDP and monthly coincident business cycle indicators. The resulting index is related to latent monthly real GDP. Copyright © 2002 John Wiley & Sons, Ltd.     

Output gap measurement and the New Keynesian Phillips curve for China

The New Keynesian Phillips curve implies that the output gap, the deviation of the actual output from its natural level due to nominal rigidities, drives the dynamics of inflation relative to expected inflation and lagged inflation. This paper exploits the empirical success of the New Keynesian Phillips curve in explaining China's inflation dynamics with a new measure of the output gap. We estimate the output gap using the Bayesian multivariate Beveridge–Nelson decomposition method, based on a multivariate dynamic model featuring distinct interactions among inflation, money, and real output in China. The empirical results using quarterly data spanning 1979–2010 show that the new measure of the output gap outperforms the traditional measures in fitting the New Keynesian Phillips curve. This result provides useful insights for inflation dynamics and monetary policy analysis in China.     

Measuring Inflation Expectations Using Interval‐Coded Data*

To quantify qualitative survey data, the Carlson–Parkin method assumes normality, a time‐invariant symmetric indifference interval, and long‐run unbiased expectations. These assumptions are unnecessary for interval‐coded data. In April 2004, the Monthly Consumer Confidence Survey in Japan started to ask households about their price expectations a year ahead in seven categories with partially known boundaries. Thus one can identify up to six parameters including an indifference interval each month. This paper compares normal, skew normal (SN), skew exponential power (SEP), and skew t (St) distributions, and finds that an St distribution fits the data well. The results help us to better understand the dynamics of heterogeneous expectations.     

A Coincident Index,Common Factors,and Monthly Real GDP*

The Stock–Watson coincident index and its subsequent extensions assume a static linear one‐factor model for the component indicators. This restrictive assumption is unnecessary if one defines a coincident index as an estimate of monthly real gross domestic products (GDP). This paper estimates Gaussian vector autoregression (VAR) and factor models for latent monthly real GDP and other coincident indicators using the observable mixed‐frequency series. For maximum likelihood estimation of a VAR model, the expectation‐maximization (EM) algorithm helps in finding a good starting value for a quasi‐Newton method. The smoothed estimate of latent monthly real GDP is a natural extension of the Stock–Watson coincident index.     

Measuring the natural rates,gaps, and deviation cycles

One definition of the natural rate is the (time-varying) steady state equilibrium rate. Then the gap is the difference between the actual and natural rates, or the forecastable movement. Although modern business cycle theories study deviation cycles (cycles in the gap), the NBER business cycle reference dates measure classical cycles (cycles in the actual rate) in the US. Measuring deviation cycles requires detrending, and this motivated the invention of the Beveridge–Nelson (B–N) decomposition. This paper considers multivariate detrending, and proposes a Bayesian approach to the multivariate B–N decomposition. An application of the method to US data gives (i) a joint estimate of the natural rates and gaps of output, inflation, interest, and unemployment with reliable error bands, and (ii) the posterior probabilities of positive gap, recession, and revival. These results may help us to identify the four phases of deviation cycles: expansion, recession, contraction, and revival.     

Multivariate model-based gap measures and a new Phillips curve for China

This paper examines empirically the Phillips curve relationship for the Chinese economy. We use quarterly data that go back to 1978 and employ a multivariate rather than univariate method in the construction of gap measures for inflation, money and output jointly with reliable error bands. Our empirical results show that the inflation gap and the output gap fit a New Phillips curve very well. We also find some structural change in the inflation–output trade-off.     

Do coincident indicators have one-factor structure?

The Stock–Watson coincident index of business cycles and its extensions assume a static linear one-factor model for the component indicators. This paper tests that assumption. Since the factor structure restricts the autocovariance matrices of the component indicators, a distance test, or the Hansen–Sargan test of over-identifying restrictions, is applicable. This also gives a GMM counterpart of the Stock–Watson coincident index, or a new composite index (CI) of coincident indicators, as a by-product. For the four US coincident indicators that currently make up the CI, the test strongly rejects the null hypothesis of static linear one-factor structure.