[From Rick Marken (2004.02.01.0945)]

The following is an analysis of the U.S. Department of Commerce: Bureau of Economic Analysis quarterly data on gross private investment, gross government investment and GDP growth rate from 4/1/49 through 7/1/02. There are 214 data point in the analysis. The definition of the values used for Gross private investment is as follows:

Gross private domestic investment (1ò40) consists of fixed investment (1ò41) and change in private inventories (1ò46). Fixed investment consists of both nonresidential (1ò42) fixed investment and residential (1ò45) fixed investment. It is measured without a deduction for CFC [consumption of fixed capital] and includes replacements and additions to the capital stock. It covers all investment in fixed assets by private businesses and by nonprofit institutions in the United States, regardless of whether the fixed asset is owned by U.S. residents.

The graph below shows three variables, Ip/GDP (Gross private investment as a proportion of GDP), (Ip+Ig)/GDP (Gross government investment as a proportion of GDP) and dGDP/dt (growth rate each quarter) changing over time. The line for growth rate has been smoothed slightly by filtering to make it easier to see the relationship between growth and investment. Without the filtering, the high frequency components of the time plot of growth rate make the graph hard to read. All statistical calculations, however, were done with the 214 unfiltered quarterly growth rate values.

Visual inspection of the time plots shows that there is a clear relationship between investment and growth rate. Growth goes up when investment goes up and growth goes down when investment goes down. However, the phase relationship between the time plots for growth and investment is difficult to see in the plots. That it, it is difficult to tell whether the growth plot leads, lags or is perfectly in phase with variations in investment.

One way to evaluate the phase relationships between two time series is to do lagged correlations. A lagged correlation is the correlation between one waveform and the time displaced version of another. (I believe the lagged correlation is equivalent to a convolution integral for normalized waveforms). In this case, I correlated the growth plot with time displaced versions of the investment plots (the plot for private and total investment as a proportion of GDP). The results are shown below:

The first column is the number of time units (fiscal quarters in this case) by which the investment plot is displaced relative to the growth plot. For example, -1 means that the investment plot is shifted one time unit back with respect to the growth plot so we are looking at the correlation of investment one quarter earlier with current growth. A shift of -2 means that we are looking at the correlation of investment two quarters earlier with current growth. A shift of 0 means that we are looking at the correlation of current investment and current growth. A shift of 1 means that we are looking at the correlation of investment with growth that occurred one quarter earlier. Similarly, a shift of 2 means that we are looking at the correlation of investment with growth that occurred two quarters earlier

What the results show is that investment follows growth, not vice versa. There is actually a negative relationship between investment and growth (indicated by the negative correlations for lags -1 through -5) that peaks 4 quarters (1 year) before the present (0 lag). That is, up to four quarters prior to the present, current investment levels are increasingly negatively related to subsequent growth levels. As current investment increases, subsequent growth decreases and vice versa.

The largest positive correlation between investment and growth occurs 2 quarters after the present. That is, up to two quarters after the present, current investment levels are increasingly positively related to past growth levels. Current increases in GDP (growth) lead to future (two quarters later) increases in investment. Current decreases in GDP (contraction) lead to future (two quarters later) decreases in investment.

These results make sense from the point of view of a closed loop model of the economy. The aggregate producer would be expected increase production (by increasing investment) to meet demand (the aggregate consumer's purchasing power). The aggregate producer is controlling for getting paid back for what it produces. So it would be expected to vary production (by varying investment) to match expected consumption.

Best regards

Rick

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Richard S. Marken

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