*A Mark Sadowski post*

In this post we are going to going to enter two more currencies into the baseline VAR while including variables reflecting their individual monetary policies.

In particular we are going enter the next two currencies with the largest relative weights in the Real Trade Weighted U.S. Dollar Index: Broad (TWEXBPA), namely the Mexican peso (11.9%) and the Japanese yen (6.9%). To estimate the real exchange rate (RER) 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 RERMXUS and RERJPUS.

Here are the graphs of the natural logs 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 RERMXUS ** are** cointegrated at this lag length. Recall that if two variables are cointegrated this implies that there must be Granger causality in at least one direction between them. On the other hand the Johansen’s Trace Test and the Maximum Eigenvalue Test both suggest that that the US monetary base and RERJPUS are not cointegrated.

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 Mexican peso 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 Mexican peso in terms of the US dollar at the 1% significance level.
- I reject the null that the real exchange rate of the Japanese yen in terms of the US dollar does not Granger cause the US monetary base at the 5% significance level, and I reject the null that the US monetary base does not Granger cause the real exchange rate of the Japanese yen in terms of the US dollar at the 10% significance level.

In other words there is strong evidence that the US monetary base Granger causes the real exchange rate of the Mexican peso in terms of the US dollar but not the other way around, and there is evidence of bidirectional Granger causality between the US monetary base and the real exchange rate of the Japanese yen in terms of the US dollar.

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 (Choleskey 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 Mexican monetary base, the Mexican bank funding rate, the effective fed funds rate and the log of the real exchange rate of the Mexican peso in terms of the US dollar added to the baseline VAR model, a majority of the information criteria suggest a maximum lag length of three. 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 three cointegrating equations at this lag length, and the Maximum Eigenvalue Test indicates that there are four. In any case, this is expected, since we already have evidence that the US monetary base is cointegrated with both industrial production and the real exchange rate of the Mexican peso 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 Japanese monetary base, the Japanese call rate, the effective fed funds rate and the log of the real exchange rate of the Japanese yen in terms of the US dollar added to the baseline VAR model, a plurality of information criteria suggest a maximum lag length of either one or four. An LM test suggests that there is a problem with serial correlation at any lag length less than four. 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 is one. In any case, this is expected, since we already have evidence that the US monetary base is cointegrated with industrial production.

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 US monetary base and to real exchanges rates in the seven-variable VARs.

The instantaneous response of the real exchange rate of the Mexican peso 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 months two and three. Furthermore, a positive shock to the real exchange rate of the Mexican peso in terms of the US dollar in month one leads to a statistically significant positive response in the level of industrial production in months three through six.

The instantaneous response of the real exchange rate of the Japanese yen 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 months six through ten. Furthermore, a positive shock to the real exchange rate of the Japanese yen in terms of the US dollar in month one leads to a statistically significant positive response in the price level in months three through five.

The IRFs also show that a positive 2.5% shock to the US monetary base in month one leads to a peak increase in the real exchange rate of the Mexican peso in terms of the US dollar of 1.1% in month three. In turn, a positive 2.5% shock to real exchange rate of the Mexican peso in terms of the US dollar in month one leads to a peak increase in industrial production of 0.15% in month five.

The IRFs also 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 Japanese yen in terms of the US dollar of 1.1% in month seven. In turn, a positive 2.1% shock to real exchange rate of the Japanese yen in terms of the US dollar in month one leads to a peak increase in the price level of 0.089% in month three.

Why do the Mexican peso and the Japanese yen 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 Mexican peso and the Japanese yen in terms of the US dollar.

Why might an increase in the real exchange rate of the Mexican peso and the Japanese yen in terms of the US dollar lead to an increase in the US output level or price level?

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 it can raise the price of goods and services imported from that currency area, which may be reflected by an increase in the US price level.

In my next post I shall add commercial bank deposits to the baseline VAR. Do positive shocks to the monetary base affect the quantity of commercial bank deposits? And does the amount of commercial bank deposits have an effect on the output level and the price level?

Tune in next time and find out.