The Monetary Base and the Channels of Monetary Transmission in the Age of ZIRP: Conclusion

A Mark Sadowski post

  1. The Object of This Exercise

One point of this series of posts (see list at the end) was to show that during the US age of zero interest rate policy (ZIRP) from December 2008 through May 2015, using nothing more complicated than a simple conventional Vector Auto-Regression (VAR) model with a minimum of structure, the monetary base has had statistically significant effects on the goods and services markets through broad spectrum of financial market variables. The other is that we now have a baseline VAR model that can be used for further policy analysis, and which can be improved in the future through the use of different impulse response identification structures, or perhaps more advanced estimation methods.

  1. Why the Monetary Base?

The monetary base is unique among monetary aggregates in that the central bank has the ability to decide precisely how large it will be at any given moment. Even the amount of bank reserves, which along with currency in circulation is a component of the monetary base, cannot be determined with any precision by the central bank, since it is a residual of the amount of currency in circulation, which is itself determined by the depositors’ desire to hold currency. The only other variable which the central bank can arguably target with such precision is the overnight interbank lending rate, which is itself largely determined by the size of the monetary base through the conduct of open market operations.

Thus, if one is interested in studying the effects of monetary policy at the zero lower bound in short term interest rates, the monetary base is the logical variable to represent the instrument of monetary policy. The fact that, away from the zero lower bound, the usual instrument of monetary policy, namely the overnight interbank lending rate, is itself essentially determined by the size of the monetary base, means that this change in instrument during the age of zero interest rate policy (ZIRP) is less meaningful than many may realize.

And, it is worth noting, any monetary economics model that uses as its primary monetary variable one which cannot be easily controlled by the central bank is, quite simply, useless for studying the effects of monetary policy.

  1. The Importance of Proper Model Specification

In each of these posts I have discussed in detail the types of diagnostics that I have conducted in fitting the model to the data. The reason for this is two-fold.

One is that I wanted these posts, as technical as they may at times seem to be, to be highly accessible. That is, I want these results to be easily reproducible by anyone who has the time series econometric background and access to commonly used econometric software packages such as EViews, Stata, SAS, R, Gretl, etc. If I am doing anything at all novel here, it is to as much as possible enable others to verify these results for themselves.

Second, without proper model specification, the obtained results almost certainly will be statistically biased, meaning that the reported statistical significance of the results, if any, will be highly questionable.

And if a time series model’s results are reported without routine references their statistical significance, then they should always be viewed with deep skepticism.

  1. Other Channels of Monetary Transmission

The three most important channels of money transmission that I didn’t directly address in this series of posts are 1) the Traditional Real Interest Rate Effects Channel, 2) the excess bank reserve channel of the Bank Lending Channel, and 3) the Cash Flow Channel.

According to the Traditional Real Interest Rate Effects Channel, reductions in the expected long-term real interest rate lead to increased expenditures on physical investment and durable goods. My own estimates indicate that during the age of zero interest rate policy (ZIRP) there is no correlation between expected long-term real interest rates (as measured by the 10-Year Treasury Inflation-Indexed Security) and industrial production or the price level. Moreover there’s no correlation between the monetary base and expected long-term real interest rates.

According to the excess bank reserves channel of the Bank Lending Channel, a rise in excess reserves leads to an increase in bank lending. My own estimates indicate that there is in fact a correlation between excess bank reserves and bank credit, but that this correlation is hard to disentangle from the other channels through which changes in the monetary basis appear to be influence bank credit, namely the balance sheet channel and the household liquidity effects channel. Moreover, I am skeptical that an increase in bank reserves would have much of a marginal effect on the amount of bank credit. In any case, regardless of how changes to the monetary base are influencing the amount of bank credit, the effect is statistically significant. The more important problem is of course that the level of bank credit does not have a statistically significant effect on output or prices.

According to the Cash Flow Channel, reductions in nominal interest rates lead to increase the liquidity of debtor households and firms at the expense of creditor households and firms. The interest rate that is most representative of this effect is the 10-Year Treasury Security yield. As we saw in the post on the Bond Yield Channel, positive shocks to the monetary base lead to increases in the 10-Year Treasury Security yield, the opposite of what the effect of expansionary monetary policy is theorized to be under the Cash Flow Channel. Furthermore, increases in the 10-Year Treasury Security yield lead to increases in industrial production, the opposite effect of what is implicitly theorized under the Cash Flow Channel.

Is there reason to believe that these three channels of monetary transmission work away from the zero lower bound in short term interest rates? The short answer is no.

Many researchers, including Bernanke and Gertler (1995), believe that empirical evidence does not support strong interest rate effects operating through the cost of physical capital, as is theorized under the Traditional Real Interest Rate Effects Channel. My own estimates from during times when the US economy has been away from the zero lower bound in short-term interest rates show that while there is a correlation between the ex-post real (i.e. adjusted by the year on year PCEPI) 10-Year Treasury Security yield and private nonresidential investment and private residential investment, there is no correlation with durable goods spending. More importantly, I find that higher real interest rates lead to higher physical investment spending, not lower. That only really makes sense in a model that acknowledges the role of money in determining interest rates.

As for the excess bank reserves channel, several studies have shown that during times when the central bank is targeting the overnight interbank interest rate as its instrument of monetary policy, bank credit usually Granger causes the monetary base. This is often misinterpreted by endogenous money enthusiasts as meaning that the actions of the central bank are constrained by the demand for bank credit. The reality is that when the central bank targets an interest rate, the level of bank credit and the monetary base (and practically everything in the economy for that matter) are endogenous to the central bank’s interest rate target. The reason why I bring this up however is that away from the zero lower bound in short term interest rates there is little reason to believe that it is the level of excess bank reserves that is determining the level of bank credit. Rather, it is the central bank’s interest rate target that is ultimately determining the level of bank credit.

And finally, as weak as the empirical evidence is for the theorized workings of the Cash Flow Channel during the age of ZIRP, it is even weaker during the times when the US economy has been away from the zero lower bound in short-term interest rates. Anyone who has taken note of the yield curve’s obvious predictive power for business cycles knows that the correlation between nominal long term-rates and aggregate nominal spending must be the opposite of what is theorized under the Cash Flow Channel.

  1. Whither the Role of Interest Rates?

In most of these posts I was able to generate statistically significant monetary policy effects without any reference at all to an interest rate as the instrument of monetary policy. The only exception was in the posts on the Exchange Rate Channel where I found it necessary to include the overnight interbank interest rate owing to the fact that most major US trading partners have been targeting that rate as the instrument of monetary policy during the age of US ZIRP, and the real exchange rate is determined not only by the monetary policy of the domestic country, but also by the foreign trade partner.

However, as we have just discussed, the empirical evidence does not support the Traditional Real Interest Rate Channel, and the empirical evidence flatly contradicts the supposed workings of the Cash Flow Channel, and these two are the only other monetary transmission channels that rely at all on interest rates. Thus we are left with the realization that interest rates are only important to the extent that they are targeted by the central bank, and even then their importance seems to be primarily stemming from what it indicates about what is happening to the monetary base.

  1. Does the Liquidity Trap Exist?

Modern applied macroeconomic models of the liquidity trap usually rely on some version of the David Romer’s ISLM/ISMP model.

If expected short-term real interest rates cannot be lowered to a level prescribed by some version of a Taylor Rule, the only way to increase real output is by increasing inflation expectations. This is because the central bank can only determine the level of real output through changes in the expected short-term real interest rate.

But as we have seen here there is really is no monetary transmission channel that works primarily, much less exclusively, through expected short-term interest rates. Thus any model that relies on the supposed inability of the central bank to lower expected short-term interest rates to demonstrate the ineffectiveness of monetary policy is guilty of assuming its conclusion.

Central banks usually target short term interest rates as an instrument of monetary policy not because there is any credible mechanism by which they directly and significantly impact the economy, but because 1) they are quickly and accurately measurable, 2) the central bank can exercise a great deal of control over them, and 3) because changes in them usually lead to reasonably predictable outcomes in terms of policy goals. These qualities may make short term interest rates convenient as an instrument of monetary policy away from the zero lower bound, but they should in no way cause us to confuse short-term interest rates for the actual mechanisms by which monetary policy is transmitted.

  1. Are There Other Reasons to Believe in the Liquidity Trap?

The most popular way to “prove” the existence of the liquidity trap is to simply point at a graph of the monetary base of a country in ZIRP (and/or the velocity of the monetary base) and then profoundly intone, “see?” But all this really shows is that the velocity of the monetary base is a variable, something which every applied macroeconomist already knows.

And an argument consisting of little more than a line graph depicting the time series of values of a quantity should never be accepted as a proof of anything, except that the person who is arguing that it proves something is not familiar with what constitutes acceptable empirical evidence, is incapable of understanding what constitutes acceptable empirical evidence, or is simply willfully ignoring what constitutes acceptable empirical evidence because it contradicts their preferred model.

The series of posts:1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,

 

The Monetary Base and the Bank Lending Channel of Monetary Transmission in the Age of ZIRP

A Mark Sadowski post

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

In particular, we are going to add Bank Credit at All Commercial Banks (LOANINV).

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

Sadowski GC11_1

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 four. 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 unstable at this lag length, and increasing the lag length does not seem to fix the issue. This would be a problem if our primary objective in estimating the bivariate VAR was look at its impulse response functions (IRFs). Fortunately, the Granger causality test results do not rely on the bivariate VAR being dynamically stable. Finally, 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 bank credit.

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 5, I left the intervals at 1 to 4 and declared the lag of each variable to be exogenous variables. Here are the Granger causality test results.

Sadowski GC11_2

Thus I fail to reject the null hypothesis that bank credit does not Granger cause the monetary base, but I reject the null hypothesis that the monetary base does not Granger cause bank credit at the 5% significance level. In other words there is evidence that the monetary base Granger causes bank credit, but not the other way around.

Since the monetary base Granger causes bank credit, 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 bank credit.

With the bank credit added to the baseline VAR model, most 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 four-variable VAR to be dynamically stable.

The Johansen’s Trace Test and Maximum Eigenvalue Test both indicate that there exists two cointegrating equations at this lag length. But this is expected, since we already have evidence that the monetary base is cointegrated with both industrial production and bank credit. This matter is addressed in greater detail in the three posts where the baseline VAR is developed.

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 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. Here are the responses to the monetary base and to bank credit in the four-variable VAR.

Sadowski GC11_3

The instantaneous response of bank credit to a positive shock to the monetary base is negative, but it is relatively small and is statistically insignificant. This is followed by a statistically significant positive response in months 11 through 18. However, a positive shock to bank credit does not lead to a statistically significant response in either the level of industrial production or the price level in any month.

The IRFs show that a positive 2.2% shock to the monetary base in month one leads to a peak increase in bank credit of 0.32% in month 14.

So why might an increase in the monetary base lead to an increase in bank credit?

A positive shock to the monetary base raises Nominal GDP (NGDP) expectations, which as we saw in this post, leads to higher stock prices. Higher stock prices raise the net worth of firms, which lowers the perception of adverse selection and moral hazard problems, which makes it more likely that banks will lend for physical investment spending. This so-called balance sheet channel has been amply described in surveys by Bernanke and Gertler (1995), Cecchetti (1995), and Hubbard (1995).

The firm balance sheet channel has its counterpart in the household liquidity effects channel. When stock prices rise, the value of financial assets rise, and consumer borrowing for durable expenditures rise because consumers have a more secure financial position and decreased expectations of suffering financial distress. The household liquidity effects channel was found to be an important factor by Mishkin (1978) during the Great Depression.

But why hasn’t the positive response of bank credit to positive shocks to the monetary base had a statistically significant affect on the level of industrial production or the price level during the age of zero interest rate policy (ZIRP)?

One possibility is that the financial crisis rendered the bank lending channel less effective than it otherwise would be.

But a more likely possibility is simply that nominal spending causes nominal lending, and not the other way around.

Thus the response of the output level and the price level to increased NGDP expectations would be the same regardless of the level of bank lending.

In my next post I will discuss the main conclusions and implications of this series.

The Monetary Base and the Bank Deposit Channel of Monetary Transmission in the Age of ZIRP

A Mark Sadowski post

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

In particular, we are going to add Deposits, All Commercial Banks (DPSACBM027SBOG).

The first thing I want to do is to demonstrate that the monetary base Granger causes bank deposits during the period from December 2008 through May 2015. Here is a graph of the natural log of SBASENS and DPSACBM027SBOG.

Sadowski GC10_1

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 not cointegrated at this lag length.

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.

Sadowski GC10_2

Thus I fail to reject the null hypothesis that bank deposits do not Granger cause the monetary base, but I reject the null hypothesis that the monetary base does not Granger cause bank deposits at the 10% significance level. In other words there is evidence that the monetary base Granger causes bank deposits, but not the other way around.

Since the monetary base Granger causes bank deposits, 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 bank deposits.

With the bank deposits added to the baseline VAR model, most information criteria suggest a maximum lag length of two. An LM test suggests that there is a problem with serial correlation at this lag length, but this problem disappears when the lag length is increased to four. An AR roots table shows the VAR to be dynamically stable.

The Johansen’s Trace Test indicates that there exists two cointegrating equations, and the Maximum Eigenvalue Test indicates that there exists one cointegrating equation at this lag length. In any case, this is expected, since we already have evidence that the monetary base is cointegrated with industrial production. 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. Here are the responses to the monetary base and to bank deposits in the four-variable VAR.

Sadowski GC10_3

The instantaneous response of bank deposits to a positive shock to the monetary base is positive, but statistically insignificant. This is followed by a statistically significant positive response in months two and three. However, a positive shock to bank deposits does not lead to a statistically significant response in either the level of industrial production or the price level in any month.

The IRFs show that a positive 2.2% shock to the monetary base in month one leads to a peak increase in bank deposits of 0.24% in month three.

So why might an increase in the monetary base lead to an increase in bank deposits?

If the Federal Reserve purchases a Treasury or an Agency security from a nonbank, the money received by the nonbank is either deposited into a bank or it is retained as currency. Since banks have nearly consistently increased their holdings of Treasury and Agency securities throughout this time period, purchases of Treasury and Agency securities by the Federal Reserve have probably mostly ended up adding to the amount of bank deposits.

Why hasn’t the increase in bank deposits led to a more statistically significant increase in the level of industrial production or the price level during the age of zero interest rate policy (ZIRP)? I’m not sure, but it certainly is a challenge for those who believe that broad money has more explanatory power than the monetary base.

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

Tune in next time and find out.

The Monetary Base and the Exchange Rate Channel of Monetary Transmission in the Age of ZIRP: Part 3

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.

Sadowski GC9_1

Sadowski GC9_2

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.

Sadowski GC9_3

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.

Sadowski GC9_4

Sadowski GC9_5

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.

The Monetary Base and the Exchange Rate Channel of Monetary Transmission in the Age of ZIRP: Part 2

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.

Sadowski GC8_1

Sadowski GC8_2

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 are 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.

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.

Sadowski GC8_3

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.

Sadowski GC8_4

Sadowski GC8_5

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.

 

The Monetary Base and the Exchange Rate Channel of Monetary Transmission in the Age of ZIRP: Part 1

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.

Sadowski GC7_1

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.

Sadowski GC7_2

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.

Sadowski GC7_3

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.

Sadowski GC7_4

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.

 

The Monetary Base and the Stock Price Channel of Monetary Transmission in the Age of ZIRP

A Mark Sadowski post

In this post we are going to add US stock market indices to the baseline VAR which I developed in these three posts. (1, 2, 3).

In particular, we are going to add the Dow Jones Industrial Average (DJIA) and the S&P 500 Index (SP500).

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

Sadowski GC6_1

And here is a graph of the natural log of SBASENS and SP500.

Sadowski GC6_2

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 the VAR that includes the Dow Jones Industrial Average as a variable. 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 not cointegrated at this lag length.

Most information criteria suggest a maximum lag length of five for the VAR that includes the S&P 500 Index as a variable. 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 at this lag length, and 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 two 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.

Sadowski GC6_3

Thus, the results are as follows:

  • I fail to reject the null that the Dow Jones Industrial Average does not Granger cause the monetary base, but I reject the null that the monetary base does not Granger cause the Dow Jones Industrial Average at the 1% significance level.
  • I fail to reject the null that the S&P 500 Index does not Granger cause the monetary base, but I reject the null that the monetary base does not Granger cause the S&P 500 Average at the 1% significance level.

In other words there is strong evidence that the monetary base Granger causes stock market indices, but not the other way around.

Since the monetary base Granger causes stock market indices they 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 stock market indices.

With the Dow Jones Industrial Average added to the baseline VAR model, most information criteria suggest a maximum lag length of three. However, an LM test suggests that there is problem with serial correlation at this lag length. Increasing the lag length to four eliminates this problem. An AR roots table shows the VAR to be dynamically stable.

With the S&P 500 Index added to the baseline VAR model, most information criteria suggest a maximum lag length of three. However, an LM test suggests that there is problem with serial correlation at this lag length. Increasing the lag length to four eliminates this problem. An AR roots table shows the VAR to be dynamically stable.

The Johansen’s Trace Test and Maximum Eigenvalue Test both indicate that there exists one cointegrating equation at this lag length in both VARs. But this is expected, since we already have evidence that the monetary base is cointegrated with industrial production. This matter is addressed in greater detail in the three posts where the baseline VAR is developed.

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 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. Here are the responses to the monetary base and the stock market indices in the four-variable VARs.

Sadowski GC6_4

Sadowski GC6_5

The response of the Dow Jones Industrial Average to a positive shock to the monetary base is significantly positive from month one through month three. The instantaneous response of the S&P 500 Index is positive but statistically insignificant. This is followed by a statistically significant positive response in month two. Furthermore a positive shock to the Dow Jones Industrial Average in month one leads to a statistically significant positive response in the level of industrial production in months four through eight, and a positive shock to the S&P 500 Index in month one leads to a statistically significant positive response in the level of industrial production from months five through eight.

The IRFs show that a positive 2.3% shock to the monetary base in month one leads to a peak increase in the Dow Jones Industrial Average of 1.6% in month three. In turn, a positive 2.3% shock to the Dow Jones Industrial Average in month one leads to a peak increase in industrial production of 0.15% in month five.

The IRFs also show that a positive 2.2% shock to the monetary base in month one leads to a peak increase in the S&P 500 Index of 1.5% in month three. In turn, a positive 2.7% shock to the S&P 500 Index in month one leads to a peak increase in industrial production of 0.17% in month eight.

That Quantitative Easing (QE) raises stock prices is probably one of the least controversial claims about it. In fact, perhaps one of the most iconic images in the age of zero interest rate policy (ZIRP) is the series of graphs concerning the relationship between the S&P 500 Index and QE posted by Bill McBride of Calculated Risk, such as this one. (The references to “Operation Twist” are, if anything, a distraction.)

Sadowski GC6_6

Nominal stock prices have probably risen in response to positive shocks to the monetary base due to higher Nominal GDP (NGDP) expectations.

So the real question is why might higher stock prices lead to higher output?

James Tobin’s q theory provides one mechanism through which increased NGDP expectations may increase output 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 and structures 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 and structures they are buying. Thus nominal investment spending will rise because corporations can purchase new equipment and structures with only a small issue of stock.

Franco Modigliani’s life-cycle theory of consumption provides another mechanism through which increased NGDP expectations may increase output through its effects on the prices of stocks. In the life-cycle model, consumption spending is determined by the expected resources of consumers, which are made up of human capital, physical capital and financial wealth. A major component of financial wealth is the holdings of stock shares. When stock prices increase, the value of financial wealth increases, thus increasing the expected resources of consumers, and nominal consumption spending rises.

The bottom line is, in the Age of ZIRP, positive shocks to the monetary have probably raised NGDP expectations, which has raised stock prices, which has increased nominal investment and consumption spending, which has raised real output.

Next time I shall add a measure of the value of the dollar to the baseline VAR. How has QE affected the value of the dollar, and how have changes in the value of the dollar impacted the economy?

Tune in next time and find out.

 

 

 

The Monetary Base and the Bond Yield Channel of Monetary Transmission in the Age of ZIRP

A Mark Sadowski post

In this post we are going to add US bond yields to the baseline VAR which I developed in these three posts (here, here & here).

In particular, we are going to add the yield of 10-Year Treasury Constant Maturity Securities (GS10) and yield of Moody’s Seasoned Aaa Corporate Bonds (AAA).

The first thing I want to do is to demonstrate that the monetary base Granger causes bond yields during the period from December 2008 through May 2015. Here is a graph of the natural log of SBASENS and of GS10 measured in percent.

Sadowski GC5_1

And here is a graph of the natural log of SBASENS and of AAA measured in percent

Sadowski GC5_2

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 the VAR that includes 10-year Treasury Bond yields as a variable. 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 not cointegrated at this lag length.

Most information criteria suggest a maximum lag length of five for the VAR that includes Aaa Corporate Bond yields as a variable. The LM test suggests that there is a problem with serial correlation, but this problem disappears when the lag length is increased to six. The AR roots table suggests that the VAR is dynamically stable at this lag length, and 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 two 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 and 1 to 7 respectively, I left the intervals at 1 to 2 and 1 to 6 and declared the lag of each variable to be exogenous variables. Here are the Granger causality test results.

Sadowski GC5_3

Thus, the results are as follows:

  • I fail to reject the null that 10-year Treasury Bond yields does not Granger cause the monetary base, but I reject the null that the monetary base does not Granger cause 10-year Treasury Bond yields at the 5% significance level.
  • I fail to reject the null that Aaa Corporate Bond yields does not Granger cause the monetary base, but I reject the null that the monetary base does not Granger cause Aaa Corporate Bond yields at the 1% significance level.

In other words there is strong evidence that the monetary base Granger causes bond yields, but not the other way around.

Since the monetary base Granger causes bond yields they 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 bond yields.

With 10-year Treasury Bond yields added to the baseline VAR model, most information criteria suggest a maximum lag length of three. However, an LM test suggests that there is problem with serial correlation at this lag length. Increasing the lag length to four eliminates this problem. An AR roots table shows the VAR to be dynamically stable.

With Aaa Corporate Bond yields 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 and Maximum Eigenvalue Test both indicate that there exists one cointegrating equation at this lag length in both VARs. But this is expected, since we already have evidence that the monetary base is cointegrated with industrial production. 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. Here are the responses to the monetary base and bond yields in the four-variable VARs.

Sadowski GC5_4

Sadowski GC5_5

The instantaneous response of bond yields to a positive shock to the monetary base is positive, but statistically insignificant in both cases. This is followed by a statistically significant positive response in the third and fourth month. Furthermore a positive shock to 10-year Treasury Bond yields in month one leads to a statistically significant positive response in the level of industrial production in months three and four, and a positive shock to Aaa Corporate Bond yields in month one leads to a statistically significant positive response in the level of industrial production from months three through five.

The IRFs show that a positive 2.1% shock to the monetary base in month one leads to a peak increase in 10-year Treasury Bond yields of 0.13 percentage points in month four. In turn, a positive 0.17 percentage point shock to 10-year Treasury Bond yields in month one leads to a peak increase in industrial production of 0.19% in month ten.

The IRFs also show that a positive 2.2% shock to the monetary base in month one leads to a peak increase in Aaa Corporate Bond yields of 0.097 percentage points in month four. In turn, a positive 0.13 percentage point shock to Aaa Corporate Bond yields in month one leads to a peak increase in industrial production of 0.21% in month thirteen.

So Quantitative Easing (QE) raises 10-year Treasury Bond and Aaa Corporate Bond yields?!?

Yes, in fact Michael Darda has repeatedly shown that long-term Treasury yields have generally risen under QE programs in figures such as the following.

Sadowski GC5_6

Confusingly, this runs counter to the stated objectives of the Federal Reserve’s Large Scale Asset Purchase Program (LSAP).

If the Federal Reserve purchases 10-year Treasury Bonds in large quantities that should drive the price of 10-year Treasury Bonds up and their yields down, right? Wrong!

That would be true if households or firms did that. But when the Federal Reserve increases the monetary base to purchase 10-year Treasury Bonds it increases expected Nominal GDP (NGDP), or expected aggregate demand (AD), and higher expected AD means higher inflation expectations, ceteris paribus.

Why might an increase in inflation expectations lead to an increase in bond yields? Well one reason would be that an increase in inflation expectations lowers the expected return for bonds causing the demand for bonds to decline and their demand curves to shift to the left.

This is almost certainly true in the case of 10-year Treasury Bonds, since it is unlikely that their supply would increase endogenously to an increase in expected NGDP. Rather, as NGDP increases it is more likely that the quantity supplied of 10-year Treasury Bonds will decrease, as Federal tax revenues increase, and Federal spending on social insurance, such as unemployment compensation, decreases, resulting in a decrease in the Federal deficit. Thus whatever increased demand that the Federal Reserve created for 10-year Treasury Bonds through its LSAPs was almost certainly more than counterbalanced by decreased demand by households and firms due to increased inflation expectations.

Moreover, there is another way that increased inflation expectations may lead to an increase in bond yields. For a given interest rate, when inflation expectations increases, the expected real borrowing cost falls, hence the quantity of corporate bonds supplied increases at any given bond price and interest rate. Thus an increase in inflation expectations causes the supply of corporate bonds to increase and the supply curve to shift to the right.

Furthermore, an increase in NGDP expectations may lead to an increase in the expected profitability of physical investment opportunities. The more profitable equipment and structure investments that a corporation expects it can make, the more willing it will be to issue bonds in order to finance those investments. Thus an increase in expected NGDP may cause the supply of corporate bonds to increase and the supply curve to shift to the right, resulting in a decrease in the price of bonds and an increase in their yields.

And, pointedly, increased nominal spending on equipment and structures probably means increased real output.

Next time I shall add domestic stock market indices to the baseline VAR. I suspect that the results will be less controversial than the results on long term interest rates probably are, but who knows?

The Monetary Base and the Inflation Expectations Channel of Monetary Transmission in the Age of ZIRP

A Mark Sadowski post

In this post we are going to add US inflation expectations as measured by the difference between the yield of 5-Year Treasury Constant Maturity Securities (GS5) and the yield of 5-Year Treasury Inflation-Indexed Constant Maturity Securities (FII5) to the baseline VAR which I developed in my last three posts.

This is often referred to as the 5-Year Breakeven Inflation Rate (T5YIEM).

The first thing I want to do is to demonstrate that the monetary base Granger causes inflation expectations during the period from December 2008 through May 2015. Here is a graph of the natural log of SBASENS and of T5YIEM measured in percent.

Sadowski GC4_1

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 level of SBASENS and T5YIEM in percent including an intercept for each equation.

Most information criteria suggest a maximum lag length of two. The LM test suggests that there is a no problem with serial correlation at this lag length. The AR roots table suggests that the VAR is dynamically stable at this lag length, and 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 inflation expectations.

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 interval at 1 to 2 and declared the lag of each variable to be exogenous variables. Here are the Granger causality test results.

Sadowski GC4_2

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

Since the monetary base Granger causes inflation expectations 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 inflation expectations.

With inflation expectations added to the baseline VAR model, most information criteria suggest a maximum lag length of two. However, an LM test suggests that there is problem with serial correlation at this lag length. Increasing the lag length to three eliminates this problem. An AR roots table shows the VAR to be dynamically stable.

The Johansen’s Trace Test and Maximum Eigenvalue Test both indicate that there exists one cointegrating equation at this lag length. But this is expected, since we now have evidence that the monetary base is not only cointegrated with industrial production, but also with inflation expectations. As discussed in the posts where the baseline VAR model was developed, since there is cointegration we should probably estimate a Vector Error Correction Model (a VECM), since it can generate statistically efficient estimates without losing long-run relationships among the variables as a VAR in levels (a VARL) might. However, in cases where there is no theory which can suggest the true cointegrating relationship or how it should be interpreted, it is probably better not to estimate a VECM.

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 three-variable VAR, I arranged the output level first, the price level second, and the monetary policy instrument third 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, but that the output level and price level respond to a policy shock with one lag. For the four-variable VAR, the financial variable is ordered last, implying that financial markets respond to a policy shock with no lag. This ordering is essentially the same as Christiano et al. (1996), Edelberg and Marshall (1996), Evans and Marshall (1998), and Thorbecke (1997), which place the VAR variables in order of the goods and services markets first, the monetary policy instruments second, and the financial markets last.

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 inflation expectations in the four-variable VAR.

Sadowski GC4_3

The instantaneous response of inflation expectations to a positive shock to the monetary base is negative, but it is relatively small and statistically insignificant. This is followed by a statistically significant positive response in the third month. Furthermore a positive shock to inflation expectations in month one leads to a statistically significant positive response in the level of industrial production from months four through nine.

The IRFs show that a positive 2.6% shock to the monetary base in month one leads to a peak increase in inflation expectations of 0.048 percentage points in month three. In turn, a positive 0.10 percentage point shock to inflation expectations in month one leads to a peak increase in industrial production of 0.23% in month eight.

Why might an increase in inflation expectations lead to an increase in output?

Because debt payments are contractually fixed in nominal terms, an increase in inflation expectations should lower the expected value of liabilities in real terms. On the other hand, an increase in inflation expectations should not lower the expected value of assets in real terms. Monetary expansion that leads to an increase in inflation expectations therefore raises expected net worth, which lowers the perception of adverse selection and moral hazard problems, and leads to an increase in nominal spending and output. In fact, the view that increased inflation has an important effect on nominal spending has a long tradition in economics, and it is a key feature in the debt-deflation view of the Great Depression espoused by Irving Fisher.

Perhaps of even greater importance, inflation expectations are the closest proxy we have for nominal GDP (NGDP) expectations, or expected aggregate demand (AD), as an increase in expected AD should also lead to an increase in inflation expectations, ceteris paribus. And an increase in NGDP expectations should lead to increased nominal spending by definition.

Too bad we didn’t have a prediction market for NGDP until December 2014. But I guess it’s better late than never.

Next time I shall add nominal Treasury yields to the baseline VAR.

Everybody knows that the whole purpose of QE is to drive down nominal Treasury yields, right?

Does it? Tune in next time and find out.

A Simple Baseline VAR for Studying the US Monetary Base and the Channels of Monetary Transmission in the Age of ZIRP: Part 3

A Mark Sadowski post

In Part 1 we established that there is bidirectional Granger causality between the monetary base and CPI, PCEPI and industrial production. In Part 2, using bivariate Vector Auto-Regression (VAR) models to generate Impulse Response Functions (IRFs), we showed that a shock to the monetary base leads to an increase in the price and output level. In Part 3 we are going to estimate a trivariate VAR model to verify that the relationships we observed in Part 2 are robust to the inclusion of all three types of variables.

The first thing we have to do is to put all three types of variables into VARs in levels (VARLs) and test for cointegration.

Most information criteria suggest a maximum lag length of four for both the VARL that includes CPI as the measure of the price level, and the VARL that includes PCEPI as the measure of the price level. An LM test suggests that there is no problem with serial correlation in either VARL at this lag length. The AR roots tables suggest that the VARLs are dynamically stable, and the Johansen’s Trace Test and Maximum  Eigenvalue Test both indicate that there exists one cointegrating equation in each VARL at this lag length. This probably shouldn’t be too surprising since we already have evidence that the monetary base and industrial production are cointegrated.

So, to reiterate what I argued in Part 2, although the order of integration for the log levels of all four of our series (SBASENS, CPI, PCEPI and INDPRO) is one, the fact that there is a cointegrating relationship between the three types of variables means that only estimating a VAR in first differences (a VARD) would discard the information contained in the levels and lead to model misspecification. Furthermore, since there is cointegration, we should probably estimate a Vector Error Correction Model (a VECM), since it can generate statistically efficient estimates without losing long-run relationships among the variables, as a VARL might. However, in cases where there is no theory which can suggest the true cointegrating relationship or how it should be interpreted, it is probably better not to estimate a VECM.

However, in the interests of thoroughness, I am going to estimate a VARD, a VARL and a VECM. And since we have two measures of the price level that means we will be estimating six models. But after we have done that, and have noted the results, the choice, at least for the moment, will come down to one between the two VARLs.

First, let’s estimate the VARDs. Most information criteria suggest a maximum lag length of three in both VARDs. The LM tests suggest that there is no problem with serial correlation at this lag length. And the AR roots tables suggest that both VARDs are dynamically stable at this lag length.

As I did in Part 2, I am going to use 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. I will follow the traditional practice of ordering output level first, the price level second, and the monetary policy instrument third in each vector. Changing the ordering of the variables would change the results (in this case there are six permutations), but since order doesn’t matter in the other impulse definitions I am mentioning (Residual and Generalized Impulses), we should be able to detect if this would have a significant effect. As before, the response standard errors I will show are analytic, since Monte Carlo standard errors change each time an IRF is generated.

Here are the responses to a shock to the monetary base in the trivariate VARD using CPI as the measure of the price level. I’ll restrict the time period to 10 months as it isn’t of interest after that point.

Sadowski GC3_1

And here are responses to a shock to the monetary base in the trivariate VARD using PCEPI as the measure of the price level.

Sadowski GC3_2

In each case a positive shock to the rate of change in the monetary base generates a statistically significant negative response to the rate of change in industrial production in the third month, followed by a statistically significant positive response in the fourth month as well as a statistically significant positive response to the rate of change in the price level (i.e. the inflation rate) in the third month. Changing the impulse definition to Residual or Generalized Impulse doesn’t change the results much, if at all.

Now let’s look at the IRFs for the VARLs. As I already noted, most information criteria suggest a maximum lag length of four in both VARLs, the LM tests suggest that there is no problem with serial correlation at this lag length in either of these VARLs and the AR roots tables suggest that both VARLs are dynamically stable at this lag length.

Here are the responses to a shock to the monetary base in the trivariate VARL using CPI as the measure of the price level. In this case I’ll extend the time period to 48 months.

Sadowski GC3_3

And here are responses to a shock to the monetary base in the trivariate VARL using PCEPI as the measure of the price level.

Sadowski GC3_4

In both cases a positive shock to the rate of change in the monetary base generates a statistically significant negative response to the rate of change in industrial production in the third month. With PCEPI as the measure of the price level this is followed by a statistically significant positive response in the tenth month. In both cases a positive shock to the monetary base generates a statistically significant positive response to the price level in months three and four.

Changing the impulse definition to Residual doesn’t change the results much, if at all. However changing the impulse definition to Generalized Impulse results in a statistically significant positive response in only month four in the VARL with CPI as the measure of the price level, and results in the loss of the statistically significant positive response to industrial production in the VARL with PCEPI as the measure of the price level. Note that we’ve already established that the monetary base has a statistically significant positive effect on industrial production with the VARDs. As I said in Part 2, there is loss in statistical efficiency when estimating a VARL with unit roots.

The IRFs show that a positive 2.3% shock to the monetary base in month one leads to a peak increase in industrial production of 0.26% in month 11 in the VARL that uses CPI as the measure of the price level, and that a positive 2.4% shock to the monetary base in month one leads to a peak increase in industrial production of 0.27% in month 11 in the VARL that uses PCEPI as the measure of the price level. The IRFs also show that a 2.3% and 2.4% shock to the monetary base in month one leads to a peak increase in the CPI level of 0.10% and in the PCEPI level of 0.077% in month four respectively.

Now let’s estimate the VECMs. The following IRFs are generated assuming a linear trend in the data and an intercept but no trend in the cointegrating vector. Here are responses to a shock to the monetary base in the trivariate VECM using CPI as the measure of the price level. (As I noted in Part 2, unfortunately VECM standard errors are not available in EViews.).

Sadowski GC3_5

Here are responses to a shock to the monetary base in the trivariate VECM using PCEPI as the measure of the price level.

Sadowski GC3_6

In both cases a positive shock to the monetary base generates a negative response to level of industrial production in the second through fourth month, followed by a positive response thereafter. In both cases a 2.3% positive shock to the monetary base in month one leads to a peak increase in industrial production of 0.36% in month 14. In the first VECM, CPI has a peak increase of 0.092% in month four and then falls to a maximum decrease of 0.042% in month 16. In the second VECM, PCEPI has a peak increase of 0.069% in month four and then falls to a maximum decrease of 0.014% in month 17. In both cases changing the impulse definition to either Residual or Generalized Impulse doesn’t change the results much, if at all. But as I’ve already said, there is good reason to be skeptical of these VECMs.

Now the time has come to pick between the two VARLs.

First, the VARL that uses PCEPI as the measure of the price level has a statistically significant positive increase in the level of industrial production unlike the VARL that uses CPI as the measure of the price level. This makes the PCEPI VARL more consistent with the evidence from the more statistically efficient VARDs.

Second, since PCEPI is the deflator of the Personal Consumption Expenditure component of GDP it is arguably a better measure of the price level than the much more ad hoc CPI.

Third, and perhaps most importantly, the Federal Open Market Committee (FOMC) has used the PCEPI to frame its inflation forecasts since February 2000 (Page 4, Footnote 1) and since January 2012 the FOMC has explicitly targeted the inflation rate of PCEPI.

Thus PCEPI very likely represents a better measure of the preferences of the monetary authority as it sets the policy variable (i.e. the monetary base).

So the PCEPI VARL is the Simple Baseline VAR for Studying the US Monetary Base and the Channels of Monetary Transmission in the Age of ZIRP.

In upcoming posts I shall add other variables to the VAR that the monetary base Granger causes in the age of ZIRP, such as domestic stock indices, nominal Treasury yields, inflation expectations, the value of the dollar, and commercial bank credit and deposits.