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.