Stationarity and Cointegration Tests of the Ohlson Model

Abstract

This paper investigates the time-series properties of the Ohlson (1995) model and examines their implications for empirical studies that use time-series data but do not explicitly account for such properties. Based on a sample of 95 firms with complete data from 1958 to 1994, we show that the null hypothesis that market value and book value are nonstationary cannot be rejected for most of the sample firms. More importantly, book value and residual income do not cointegrate with market value for 80 percent of the sample firms. We demonstrate the importance and relevance of the time-series properties of the model to OLS regressions by showing that the OLS out-of-sample forecasts of market value are significantly more accurate and less biased for the cointegrated firms than for the non-cointegrated firms. We also explore methods to improve the specification of OLS regressions based on the Ohlson (1995) model and suggest that scaling the variables with lagged market value can significantly alleviate the problem with nonstationarity of the unsealed time-series data.

While the generality of our results is limited by the survivorship bias of our sample, we believe that our paper has some important implications for studies motivated by the Ohlson (1995) model. First, because market value and book value are nonstationary and book value and residual income do not cointegrate with market value for most firms, the other information variable has to be nonstationary so that a linear combination of the independent variables can cointegrate with market value. Second, direct tests of the Ohlson (1995) model through OLS regressions using time-series data are questionable because they are likely to be misspecified. This may partially explain the underestimation of market value widely documented by previous studies and the significant difference between parameters predicted by the Ohlson (1995) model and estimated from OLS regressions. Third, our results also suggest that scaling the data with lagged market value can mitigate the problems with nonstationarity. For studies using unsealed time-series data, a cointegration test should be conducted first and a sensitivity analysis based on the cointegrated sub-sample should be performed to examine whether the results based on the full sample are robust.