**A Mark Sadowski post**

In this post we are going to add a measure of the value of the US dollar to the baseline VAR which I developed in these three posts; 1,2 and 3.

In particular, we are going to add the Real Trade Weighted U.S. Dollar Index: Broad (TWEXBPA).

The first thing I want to do is to demonstrate that the monetary base Granger causes the value of the dollar during the period from December 2008 through May 2015. Here is a graph of the natural log of SBASENS and TWEXBPA.

The following analysis is performed using a technique developed by Toda and Yamamoto (1995).

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

Most information criteria suggest a maximum lag length of two. An 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** cointegrated at this lag length. This suggests that there must be Granger causality in at least one direction between the monetary base and the value of the US dollar.

Then I re-estimated the level VAR with one extra lag 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 2 and declared the lag of each variable to be exogenous variables. Here are the Granger causality test results.

Thus I fail to reject the null hypothesis that the value of the US dollar does not Granger cause the monetary base, but I reject the null hypothesis that the monetary base does not Granger cause the value of the US dollar at the 1% significance level. In other words there is strong evidence that the monetary base Granger causes the value of the US dollar, but not the other way around.

Since the monetary base Granger causes the value of the US dollar, it should probably be added to our baseline VAR model. This is because, under these circumstances, we might expect shocks to the monetary base in the VAR model to lead to statistically significant changes in the value of the US dollar.

With the value of the US dollar added to the baseline VAR model, most information criteria suggest a maximum lag length of five. An LM test suggests that there is no problem with serial correlation at this lag length. An AR roots table shows the VAR to be dynamically stable.

The Johansen’s Trace Test indicates that there exists one cointegrating equation at this lag length, but the Maximum Eigenvalue Test does not show any signs of cointegration. In any case, this is expected, since we already have evidence that the monetary base is cointegrated with both industrial production and the value of the US dollar. This matter is addressed in greater detail in the three posts where the baseline VAR is developed.

I am using a recursive identification strategy (Cholesky decomposition), which is the dominant practice in the empirical literature on the transmission of monetary policy shocks. Such a strategy means that the order of the variables affects the results. For the four-variable VARs I am arranging the output level first, the price level second, the monetary policy instrument third, and the financial variable last in the vector. This ordering assumes that the Federal Open Market Committee (FOMC) sees the current output level and price level when it sets the policy instrument, and that the output level and price level respond to a policy shock with one lag, but that financial markets respond to a policy shock with ** no lag**.

As before, the response standard errors I will show are analytic, since Monte Carlo standard errors change each time an Impulse Response Function (IRF) is generated. The variables are all multiplied by 100 to make the IRFs easier to read and interpret (as I have been doing throughout). Also, 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 also make the IRFs easier to interpret. Here are the responses to the monetary base and to LRERROWUS in the four-variable VAR.

The response of the value of foreign currency a positive shock to the monetary base is not statistically significant in any month. However a positive shock to the value of foreign currency in month one leads to a statistically significant positive response in the level of prices in months two through four. The IRFs show that a positive 0.75% shock to the value of foreign currency in month one leads to a peak increase in the price level of 0.10% in month twenty-four.

When the value of foreign currency goes up and, by extension, the value of the US dollar goes down, this raises the price of imported goods and services, and this is reflected in the aggregate price level.

What about the fact that a positive shock to the monetary base does not have a statistically significant effect on the value of foreign currency? Doesn’t that contradict the results of the Granger causality test?

Well no, not really. To see why, let’s re-estimate the VAR as a VAR in differences (a VARD). Remember there is a loss of statistical efficiency when one estimates a VAR in levels (a VARL). Most information criteria suggest a maximum lag length of three in the VARD. The LM test suggests that there no problem with serial correlation at this lag length. The AR roots table suggests that the VARD is dynamically stable at this lag length.

Here are the responses to the monetary base and to LRERROWUS in the four-variable VARD. I’ll restrict the time period to 10 months as it isn’t of interest after that point.

A positive shock to the rate of change in the monetary base generates a statistically significant positive response to the rate of change in the value of foreign currency in the second month.

So why are positive shocks to the monetary base leading to statistically significant changes in the rate of change of the value of foreign currency, but not to the level of the value of foreign currency?

The value of foreign currency in terms of dollars is not only determined by US monetary policy, it is also determined by the conduct of monetary policy in other currency zones. Among the four studies that I mentioned in very beginning of this series of posts, only Honda et al. considered the effect of Quantitative Easing (QE) on the foreign exchange rate. They also did not find a statistically significant effect in levels. But they did not go any further than that.

**A more sensible approach is to look at the effect of monetary policy on bilateral exchange rates. That way the monetary policy of the other currency zone can be incorporated into the model. **

In Part 2 I am going to disaggregate LRERROWUS into separate currencies and enter them into the baseline VAR while including variables reflecting their individual monetary policies.

Why are my comments not appearing? Censorship or just a poor user experience interface?

Neither,just the commenter not knowing where he commented!