**A Mark Sadowski post**

In Part 1 we demonstrated that Value of Manufacturers’ Shipments for Capital Goods: Nondefense Capital Goods Excluding Aircraft Industries (ANXAVS) is a monthly frequency proxy for private nonresidential investment in equipment.

In Part 2 we are going to check if inflation expectations, stock prices and the value of the US dollar are correlated with private nonresidential investment in equipment in the Age of Zero Interest Rate Policy (ZIRP). Specifically we’re going to check if the 5-Year Breakeven Inflation Rate (T5YIEM), Dow Jones Industrial Average (DJIA) and the Real Trade Weighted U.S. Dollar Index: Broad (TWEXBPA) each Granger cause ANXAVS. This analysis is performed using a technique developed by Toda and Yamamoto (1995).

First let’s consider inflation expectations. Here is T5YIEM and the natural log of ANXAVS from December 2008 through September 2015.

Using the Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests I find that the order of integration is one for T5YIEM and two for LANXAVS. I set up a two-equation Vector Auto-Regression (VAR) in the levels of the data including an intercept for each equation.

Most information criteria suggest a maximum lag length of two. The LM test suggests that there is no problem with serial correlation at this lag length. The AR roots tables suggest that the VAR is dynamically stable at this lag length, and Johansen’s Trace Test and Maximum Eigenvalue Test both indicate the series ** are **cointegrated at this lag length. This suggests that there must be Granger causality in at least one direction between T5YIEM and ANXAVS.

Then I re-estimated the level VAR with two extra lags of each variable in each equation. But rather than declare the lag interval for the two endogenous variables to be from 1 to 4, I left the intervals at 1 to 2, and declared the extra two lags of each variable to be exogenous variables. Here are the Granger causality test results.

Thus, I fail to reject the null hypothesis that private nonresidential investment in equipment does not Granger cause inflation expectations, but I reject the null hypothesis that inflation expectations does not Granger cause private nonresidential investment in equipment at the 5% significance level. In other words there is evidence that inflation expectations Granger causes private nonresidential investment in equipment from December 2008 through September 2015, but not the other way around.

Next let’s consider stock prices. Here is the natural log of DJIA and ANXAVS from December 2008 through September 2015.

Using the Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests I find that the order of integration is one for LDJIA. I set up a two-equation VAR in the levels of the data including an intercept for each equation.

Most information criteria suggest a maximum lag length of one for the VAR. The LM test suggests that there is no problem with serial correlation at this lag length. The AR roots table suggests that the VAR is dynamically stable, and the Johansen’s Trace Test and Maximum Eigenvalue Test both indicate that the two series are not cointegrated at this lag length.

Then I re-estimated the level VAR with two extra lags of each variable in each equation. But rather than declare the lag interval for the two endogenous variables to be from 1 to 3, I left the intervals at 1 to 1, and declared the extra two lags of each variable to be exogenous variables. Here are the Granger causality test results.

Thus, I fail to reject the null hypothesis that private nonresidential investment in equipment does not Granger cause stock prices, but I reject the null hypothesis that stock prices does not Granger cause private nonresidential investment in equipment at the 10% significance level. In other words there is evidence that stock prices Granger causes private nonresidential investment in equipment from December 2008 through September 2015, but not the other way around.

Finally let’s consider the value of the US dollar. Here is the natural log of TWEXBPA and ANXAVS from December 2008 through September 2015.

Using the Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests I find that the order of integration is one for LTWEXBPA. I set up a two-equation VAR in the levels of the data including an intercept for each equation.

Most information criteria suggest a maximum lag length of four for the VAR. The LM test suggests that there is no problem with serial correlation at this lag length. The AR roots table suggests that the VAR is dynamically stable, and the Johansen’s Trace Test and Maximum Eigenvalue Test both indicate that the two series are not cointegrated at this lag length.

Then I re-estimated the level VAR with two extra lags of each variable in each equation. But rather than declare the lag interval for the two endogenous variables to be from 1 to 6, I left the intervals at 1 to 4, and declared the extra two lags of each variable to be exogenous variables. Here are the Granger causality test results.

Thus, I fail to reject the null hypothesis that private nonresidential investment in equipment does not Granger cause the value of the US dollar, but I reject the null hypothesis that the value of the US dollar does not Granger cause private nonresidential investment in equipment at the 1% significance level. In other words there is evidence that the value of the US dollar Granger causes private nonresidential investment in equipment from December 2008 through September 2015, but not the other way around.

The next step in this process is to determine the nature of these “correlations”. What do positive shocks to inflation expectations, positive shocks to stock prices, and negative shocks to the value of the US dollar lead to in terms of private nonresidential investment in equipment? Do they lead to a decline in investment as Mike Spence and Kevin Warsh are implicitly claiming?

Or might they cause investment to increase (counterfactually) as Monetarists claim? In order to determine this we will estimate properly specified bivariate VARs and generate appropriate Impulse Response Functions (IRFs).

For that, tune in next time.

Sadowski: “Dow Jones Industrial Average (DJIA) and the Real Trade Weighted U.S. Dollar Index: Broad (TWEXBPA) each Granger cause ANXAVS. [Nondefense Capital Goods Excluding Aircraft Industries (ANXAVS) is a monthly frequency proxy for private nonresidential investment in equipment]”. You cannot be serious. This statement is about as serious as the 1950s maxim “what’s good for General Motors is good for America”. And the person saying that never had to run a regression analysis to prove it.