*A Mark Sadowski post*

In this post we are going to going to disaggregate LRERROWUS, which is essentially the additive inverse of the natural log of Real Trade Weighted U.S. Dollar Index: Broad (TWEXBPA), into separate currencies and enter them into the baseline VAR while including variables reflecting the individual monetary policies of their respective currency areas.

A good place to start is by considering the relative weights of the currencies in TWEXBPA.

The three currencies with the greatest weights are the Chinese renminbi (21.3%), the euro (16.4%) and the Canadian dollar (12.7%). To estimate the real exchange rate (RER) of each of these currencies in terms of the US dollar I computed the ratio of the Bank for International Settlements (BIS) Real Broad Effective Exchange Rate for each currency area divided by the BIS Real Broad Effective Exchange Rate of the US. I term these ratios RERCHUS, REREUUS and RERCAUS.

The next thing I did was check to see if the US monetary base Granger causes the RER of these currencies in terms of the US dollar during the period from December 2008 through May 2015.

Not only does the US monetary base ** not **Granger cause RERCHUS, the p-value for the non-causality test is an amazingly high 99.15%. Of course the IMF has classified the exchange rate arrangement of China as a “crawl-like arrangement” (page 6) with a “de facto exchange rate anchor to the US dollar” (see footnote) since 2007.

The Granger causality test result supports this classification, and in light of it, perhaps the exchange rate arrangement of China should really be termed a “crawl-like peg”.

In any case, to do further analysis of RERCNUS I would need to know China’s monetary base and overnight repo rate, and personally I find the website of the People’s Bank of China even less user friendly than the Bank of England’s web site used to be. So I’ll leave it until a later date, and for now, based on the near 100% value of the above p-value, I’ll assume that the outcome of my efforts will end up in grim defeat anyway.

So let us turn our attentions to the euro and the Canadian dollar, which are both classified as “free floating” by the IMF. Here are the graphs of the natural log of SBASENS and the real exchange rates.

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 all three series. I set up two two-equation VARs in the log levels of the data including an intercept for each equation.

Most information criteria suggest a maximum lag length of two for both VARs. The LM test suggests that there is no problem with serial correlation at this lag length in either VAR. The AR roots table suggests that the VARs are dynamically stable. The Johansen’s Trace Test and Maximum Eigenvalue Test both indicate that the US monetary base and REREUUS ** are** cointegrated at this lag length. The Johansen’s Trace Test indicates that the US monetary base and RERCAUS

**cointegrated at this lag length, but the Maximum Eigenvalue Test does not show any signs of cointegration. Recall that if two variables are cointegrated this implies that there must be Granger causality in at least one direction between them.**

*are*Then I re-estimated the level VARs 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, the results are as follows:

- I fail to reject the null that the real exchange rate of the euro in terms of the US dollar does not Granger cause the US monetary base, but I reject the null that the US monetary base does not Granger cause the real exchange rate of the euro in terms of the US dollar at the 5% significance level.
- I fail to reject the null that the real exchange rate of the Canadian dollar in terms of the US dollar does not Granger cause the US monetary base, but I reject the null that the US monetary base does not Granger cause the real exchange rate of the Canadian dollar in terms of the US dollar at the 1% significance level.

In other words there is strong evidence that the US monetary base Granger causes the two real exchange rates but not the other way around.

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

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 have been 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**.

In what I am about to do now, I was heavily influenced by Eichenbaum and Evans (1995).

To reflect the interaction of the monetary policies of both the US and the foreign currency area, I am going to add three more variables: the effective fed funds rate, the monetary base of foreign currency area and the effective overnight interbank rate of the foreign currency area. Following the practice of Eichenbaum and Evans, I am going to place the interest rate variable after monetary aggregate variable, and I am going to place the US monetary policy variables after the foreign monetary policy variables. Thus the order of the variables in the vector will be the level of industrial production first, the personal consumption expenditure price index second, the foreign monetary base third, the foreign effective overnight interbank rate fourth, the US monetary base fifth, the effective fed funds rate sixth, and the real exchange rate last.

With the log of the Euro Area monetary base, the Eonia rate, the effective fed funds rate and the log of the real exchange rate of the euro in terms of the US dollar added to the baseline VAR model, a plurality of the information criteria suggest a maximum lag length of either one or five. An LM test suggests that there is a problem with serial correlation at any lag length less than five. An AR roots table shows the VAR to be dynamically stable at this lag length.

The Johansen’s Trace Test indicates that there exists four cointegrating equations at this lag length, and the Maximum Eigenvalue Test indicates that there are three. In any case, this is expected, since we already have evidence that the monetary base is cointegrated with both industrial production and the real exchange rate of the euro in terms of the US dollar. The matter of cointegration is addressed in greater detail in the three posts where the baseline VAR is developed.

With the log of the Canadian monetary base, the Canadian overnight money market financing rate, the effective fed funds rate and the log of the real exchange rate of the Canadian dollar in terms of the US dollar added to the baseline VAR model, a plurality of information criteria suggest a maximum lag length of four. 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 at this lag length.

The Johansen’s Trace Test indicates that there exists five cointegrating equations at this lag length, and the Maximum Eigenvalue Test indicates that there are three. In any case, this is expected, since we already have evidence that the monetary base is cointegrated with both industrial production and the real exchange rate of the Canadian dollar in terms of the US dollar.

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. Here are the responses to the monetary base and to real exchanges rates in the seven-variable VARs.

The instantaneous response of the real exchange rate of the euro in terms of the US dollar to a positive shock to the US monetary base is negative but it is relatively small and statistically insignificant. This is followed by a statistically significant positive response in month three. However, a positive shock to the real exchange rate of the euro in terms of the US dollar does not lead to a statistically significant response in industrial production or the price level in any month.

The instantaneous response of the real exchange rate of the Canadian dollar in terms of the US dollar to a positive shock to the US monetary base is positive but statistically insignificant. This is followed by a statistically significant positive response in month two. Furthermore, a positive shock to the real exchange rate of the Canadian dollar in terms of the US dollar in month one leads to a statistically significant positive response in the level of industrial production in months five and six, and a statistically significant positive response in the price level in month two.

The IRFs show that a positive 2.0% shock to the US monetary base in month one leads to a peak increase in the real exchange rate of the euro in terms of the US dollar of 1.5% in month seven. The IRFs also show that a positive 1.9% shock to the US monetary base in month one leads to a peak increase in the real exchange rate of the Canadian dollar in terms of the US dollar of 0.59% in month three. In turn, a positive 1.4% shock to real exchange rate of the Canadian dollar in terms of the US dollar in month one leads to a peak increase in industrial production of 0.10% in month six, and to a peak increase in the price level of 0.037% in month two.

Why do the euro and the Canadian dollar appreciate with respect to the US dollar in response to a positive shock to the US monetary base?

A positive shock to the US monetary base increases expected Nominal GDP (NGDP), or expected aggregate demand (AD), and higher expected AD means higher inflation expectations, ceteris paribus. This leads to an increase in the expected real exchange rates of the euro and the Canadian dollar in terms of the US dollar.

Why might an increase in the real exchange rate of the Canadian dollar in terms of the US dollar lead to an increase in the US output level and the price level?

An increase in the real exchange rate of a the Canadian dollar in terms of the US dollar makes US goods and services more competitive with Canadian goods and services, both here and in Canada, and it raises the price of goods and services imported from Canada, which is reflected by an increase in the US price level.

For the sake of thoroughness, in Part 3 I am going to enter yet two more currencies into the baseline VAR while including variables reflecting their individual monetary policies.