# QE and Business Investment: The VAR Evidence: Part 3

A Mark Sadowski post

What we are going to do next is to construct three bivariate Vector Auto-Regression (VAR) models to generate Impulse Response Functions (IRFs) in order to show what a shock to the inflation expectations, stock prices and the value of the US dollar leads to in terms of business investment. As mentioned in Part 2, all four of our series (T5YIEM, DJIA, TWEXBPA and ANXAVS) have unit roots. With unit roots in our models, we are faced with a procedure that could lead to a VAR model in differences (a VARD), a VAR model in levels (a VARL), or a Vector Error Correction Model (a VECM).

Since there is no evidence of cointegration between investment in equipment and stock prices or the value of the US dollar, we are really only faced with a choice between a VARD and a VARL in these two cases. And although the existence of cointegration between investment in equipment and inflation expectations means that a VECM is an option in the third case, given the pros and cons of doing so, I am not going to estimate a VECM. For a detailed discussion of what these pros and cons are, see this post.

This means we are confronted with a tradeoff between statistical efficiency and the potential loss of information that takes place when time series are differenced. As we shall soon see, this is not at all an issue, so in the interests of brevity, I am only going to estimate three VARLs.

Motivated by the dominant practice in the empirical literature on the transmission of monetary policy shocks, I am going to use a recursive identification strategy (Cholesky decomposition). Such a strategy means that the order of the variables affects the results. I will follow the traditional practice of ordering the goods and services market variables before the financial market variables in each vector. The response standard errors I will show are analytic, as Monte Carlo standard errors change each time an IRF is generated. In order to render the IRFs easier to interpret, for the rest of this analysis, with the exception of T5YIEM (which is already in percent) I have multiplied the log level of each series by 100.

Let’s look at the effect of a positive shock to inflation expectations first.

Most information criteria suggest a maximum lag length of two in the VAR involving inflation expectations. 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. Here are the responses to a shock to inflation expectations.

A positive shock to inflation expectations leads to a statistically significant positive response to investment in equipment in months two through 31, or a period lasting nearly two and a half years. The IRFs show that a 13 basis point shock to inflation expectation in month one leads to a peak increase in investment in equipment of 1.04% in month 11. Recall that we previously showed that a positive 2.6% shock to the monetary base (QE) leads to an increase in inflation expectations of 4.8 basis points.

Now let’s look at the effect of a positive shock to stock prices.

Most information criteria suggest a maximum lag length of one in the VAR involving stock prices. 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. Here are the responses to a shock to stock prices.

A positive shock to stock prices leads to a statistically significant positive response to investment in equipment in months two through 40, or a period lasting over three years. The IRFs show that a 3.1% shock to stock prices in month one leads to a peak increase in investment in equipment of 1.10% in month 15. Recall that we previously showed that a positive 2.3% shock to the monetary base (QE) leads to an increase in stock prices (DJIA) of 1.6%.

Finally let’s look at the effect of a negative shock to the value of the US dollar.

Most information criteria suggest a maximum lag length of four in the VAR involving the US dollar. 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. Instead of estimating the model with LTWEXBPA, I am multiplying LTWEXBPA by negative one and terming the result LRERROWUS, which stands for “real exchange rate of the rest of world in terms of the US dollar”. In other words this represents the real value of the rest of the world’s currency in terms of US dollars. This will make the IRFs easier to interpret. Here are the responses to a shock to the value of the US dollar.

A positive shock to the value of foreign currency in month one leads (with the sole exception of month 5) to a statistically significant positive response in investment in equipment in months three through 27, or a period lasting over two years. The IRFs show that a 0.90% shock to the value of foreign currency in month one leads to a peak increase in investment in equipment of 1.16% in month 25. Recall that we previously showed here and here that a positive 1.9-2.5% shock to the monetary base (QE) leads to an increase in the value of the euro (1.5%), the Canadian dollar (1.4%), the Mexican peso (1.1%) and the Japanese yen (1.1%) in terms of the US dollar.

Now that we’ve established the empirical facts concerning QE and investment in equipment, let’s discuss the monetary theory that explains these facts.

As we have previously discussed, a positive shock to the US monetary base increases expected Nominal GDP (NGDP), or expected aggregate demand (AD). Higher expected AD means higher inflation expectations, ceteris paribus. Higher expected AD also leads to higher nominal stock prices. And higher expected inflation leads to an increase in the expected real exchange rates of foreign currencies in terms of the US dollar.

So why do higher inflation expectations, higher stock prices and a lower US dollar lead to increased investment in equipment?

Inflation expectations are the closest proxy we have for expected NGDP as an increase in expected NGDP should lead to an increase in inflation expectations, ceteris paribus. An increase in expected NGDP should lead to an increase in investment in equipment as businesses anticipate rising sales and increased profit making opportunities.

James Tobin’s q theory provides a mechanism through which increased NGDP expectations lead to increased investment in equipment through its effects on the prices of stocks. Tobin defines q as the market value of corporations divided by the replacement cost of their physical capital. If q is high the market price of corporations is high relative to the replacement cost of their physical capital, and new equipment is cheap relative to the market value of corporations. Corporations can then issue stock and get a high price for it relative to the cost of the equipment they are buying. Thus investment spending will rise because corporations can purchase new equipment with only a small issue of stock.

An increase in the real exchange rate of foreign currency in terms of the US dollar can make US goods and services more competitive with goods and services priced in that currency, both here and in that currency area. And if US goods and services become more competitive with goods and services priced in foreign currencies, this provides an incentive for US businesses to increase their investment in equipment.

And what of Robert Waldmann’s theoretical argument that QE leads to less business investment by raising the price of long term Treasuries (lowering their yields)?

The biggest problem with this theory is the empirical fact, despite the widely accepted myth otherwise, that QE leads to higher bond yields.

In Waldmann’s defense, he states that he is sure that Michael Spence and Kevin Warsh are wrong, and that he is simply making a theoretical argument for their conclusion, something which DeLong and Krugman argued Spence and Warsh had failed to do.

And, something which I hitherto have not discussed, just how important is the equipment component of business investment?

The three main components of private nonresidential fixed investment (PNFI) are 1) equipment, 2) intellectual property rights, and 3) structures. In the US in 2014 PNFI totaled \$2,233.7 billion. Equipment represented \$1036.7 billion of that total or 46.4%. Intellectual property rights (software, R&D and artistic rights) represented \$690 billion of that total or 30.9%.  Structures represented \$507 billion of that total or 22.7%.

Thus equipment is by far the most important component of business investment, and I find it remarkably difficult to believe, given QE’s demonstrably positive effect on investment in equipment (as well as its demonstrably positive effect on the output and price level), that it might have a negative effect on business investment overall.

# QE and Business Investment: The VAR Evidence: Part 2

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.

# QE and Business Investment: The VAR Evidence: Part 1

A Mark Sadowski post

Mike Spence and Kevin Warsh, writing in the Wall Street Journal on Wednesday said:

“We believe that QE [Quantitative Easing] has redirected capital from the real domestic economy to financial assets at home and abroad. In this environment, it is hard to criticize companies that choose “shareholder friendly” share buybacks over investment in a new factory. But public policy shouldn’t bias investments to paper assets over investments in the real economy.”

To which Brad DeLong responded by saying:

“As I have said before and say again, weakness in overall investment is 100% due to weakness in housing investment. Is there an argument here that QE has reduced housing investment? No. Is nonresidential fixed investment below where one would expect it to be given that the overall recovery has been disappointing and capacity utilization is not high? No. The U.S. looks to have an elevated level of exports, and depressed levels of government purchases and residential investment. Given that background, one would not be surprised that business investment is merely normal–and one would not go looking for causes of a weak economy in structural factors retarding business investment. One would say, in fact, that business investment is a relatively bright spot.”

And Paul Krugman, who said:

“It is, indeed, kind of amazing. In the eyes of critics, QE is the anti-Veg-O-Matic: it does everything bad, slicing and dicing and pureeing all good things. It’s inflationary; well, maybe not, but it undermines credibility; well, maybe not but it it causes excessive risk-taking; well, maybe not but it discourages business investment, which I think is a new one.”

And Larry Summers, who said:

“Perhaps Spence and Warsh are on to something that I am missing. I’m curious whether they can point to any peer reviewed economic research, or indeed any statistical work, that backs up their views.”

And Joseph Gagnon, who said:

“…economies in which central banks were most aggressive in conducting QE early in the recovery (the United Kingdom and the United States) have been growing more strongly than economies that were slow to adopt QE (the euro area and Japan)…. Indeed, to the extent that QE has raised stock prices, it discourages businesses from buying back stock because it makes that stock more costly to buy.”

About the only economist who rose to Spence and Warsh’s defense was Robert Waldmann, who said:

“The argument is that the duration risk in long term Treasuries is negatively correlated with the risk in fixed capital. I think this is clearly true. The risk of long term Treasuries is that future short term rates will be high. This can be because of high inflation or because the FED considers high real rates required to cool off an overheated economy. Both of these are correlated with high returns on fixed capital (someone somewhere keeps arguing that what the economy needs is higher inflation).

This means that a higher price for long term treasuries should make fixed capital less attractive — the cost of insuring against the risk in fixed capital is greater.”

It just so happens that there is Vector Auto-Regression (VAR) evidence on the relationship between QE and business investment.

This summer we showed that, in the age of zero interest rate policy (ZIRP), from December 2008 to present, the monetary base Granger causes inflation expectations, stock prices and the value of the US dollar, and that positive shocks to the monetary base (QE) lead to

statistically significant increases in inflation expectations,

statistically significant increases in stock prices,

and statistically significant decreases in the value of the US dollar.

In this series of posts we are going to show that in the Age of ZIRP, inflation expectations, stock prices and the US dollar all have an effect on investment in equipment, a component of business investment.

Private nonresidential investment in equipment is only available at a quarterly frequency. So since this analysis requires data at a monthly frequency, it is necessary to find a proxy variable for investment in equipment.

In applied macroeconomics, proxy variables typically satisfy two main requirements. First, the proxy variable should measure the equivalent characteristic of a reasonable subset of the variable being proxied. Secondly, the contemporaneous growth rates of the proxy variable and the variable being proxied should be correlated (i.e. have a relatively high Pearson’s r value).

Value of Manufacturers’ Shipments for Capital Goods: Nondefense Capital Goods Excluding Aircraft Industries (ANXAVS) overlaps in content considerably with US private nonresidential investment in equipment, and is available at a monthly frequency back to January 1992. Here is a graph of the natural log of ANXAVS and the natural log of Gross Private Domestic Investment: Fixed Investment: Nonresidential: Equipment (Y033RC1Q027SBEA) since 1992Q1.

ANXAVS overlaps in content with private nonresidential investment in equipment, and it ranges from 77.4% to 116.2% of Y033RC1Q027SBEA from 1992Q1 through 2015Q3. So it would appear that the first proxy variable requirement is well satisfied.

Now we must check to see if the two variables are correlated. Here are the results of regressing the logged difference (i.e. the growth rate) of Y033RC1Q027SBEA on the logged difference of ANXAVS and the corresponding scatterplot with the Ordinary Least Squares (OLS) regression line.

The R-squared value is approximately 0.633. Since the growth rates are positively correlated, the Pearson’s r value is +0.796, which is above average for a macroeconomic proxy variable. So it would appear that the second proxy variable requirement is well satisfied. Thus we conclude that ANXAVS is a suitable monthly frequency proxy for private nonresidential investment in equipment.

In Part 2 we’ll check to see if inflation expectations, stock prices or the value of the US dollar are “correlated” with private nonresidential investment in equipment in the age of ZIRP.

# A clear call for a higher NGDP level target

Robert Samuelson writes: “The investment bust (explained)”:

One of the great disappointments of the weak economic recovery has been the sluggish revival of business investment — spending on new buildings, factories, equipment and intellectual property (mainly research and development, and software). For the United States, this spending in 2014 was about 9 percent above its 2007 record high. Sounds good? It isn’t. The average annual gain is a bit more than 1 percent over the past seven years. It is only a small stretch to say that capital has gone on strike.

Why? Can anything be done about it?

We now have a new study from the International Monetary Fund (IMF) that suggests some not very encouraging answers. For starters, it confirms that the investment bust is a global phenomenon. It’s not just the United States but also Europe, Japan and most advanced countries. As important, the main cause of the investment slump is clear-cut: Businesses aren’t expanding because they can already meet most demand with existing capacity.

“Business investment has deviated little, if at all, from what could be expected given the weakness in economic activity in recent years,” the IMF concluded.

The result is a vicious cycle: A weak economy inspires lackluster investment, and lackluster investment perpetuates a weak economy.

Could we jolt business investment from its lethargy? The IMF suggests that more economic “stimulus” (a.k.a., bigger budget deficits) would boost business investment by shrinking excess capacity. Perhaps. But it’s also possible that temporary stimulus plans — as most are — wouldn’t generate much more private investment precisely because corporate managers would see them as fleeting. Why expand to serve demand that won’t last?

If that´s not a call for a higher target level of NGDP (aggregate demand) I don´t know what is!