Structural change and phase variation: A re-examination of the q-model using wavelet exploratory analysis

This paper uses the structural change model and wavelet exploratory analysis to re-examine Tobin's q theory of investment. There are two main results. First, wavelet exploratory analysis provides a useful complementary approach to standard confirmatory statistical analysis. Specifically, using energy and time scale decomposition analyses, we find that the long-run is the dominant scale of variation for both aggregate investment and “measured” Tobin's q, and that for most of the sample there is a stable in-phase relationship between the smooth components of investment rate and q, with q slightly leading investments. Moreover, the analysis of the shift of the phase relationship of the long-term components reveals a “pure” smooth break occurring in the late 1970s, and a “spurious” smooth break in the early 1990s when the two smooth components resume their normal in-phase relationship. Second, when we combine the results from wavelet exploratory analysis and the multiple structural breaks test approach, we find that, contrary to the conventional literature, Tobin's q is an important determinant of aggregate investment, and its estimated coefficient can provide a plausible value for the implied adjustment cost of investment. Most importantly, we discover that the relationship depends on time scale; long time scales are more important than short.