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.

The following analysis is performed using a technique developed by Toda and Yamamato (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 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 interval at 1 to 2 and declared the lag of each variable to be exogenous variables. Here are the Granger causality test results.

Thus I fail to reject the null hypothesis that 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.

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.

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__Flash report: Latest stats from U.S. are that hourly wages in May are up 2.0% YOY.__

Readers bear with me, I will start with an analogy.

So, there was a married lady, who disliked sex, and thought marriage counseling was needed—for her husband. She thought he should appreciate her more-elevated virtues, her intellect, her taste in furnishings, her hostess skills, and her career. He should forget base gratifications.

Which brings to mind Martin Feldstein, Harvard econ prof, who has been preaching Inflationary End Times since at least 2009, as I pointed out in my last post here. In his last missive (June 29, for Project Syndicate) Feldstein warned wage hikes were going to run wild, threatening “accelerating” inflation. (Please note that inflation never threatens to rise to a higher level, such as 2.5%, and stay there. It always threatens to “accelerate.”)

But, the BLS just reported May wages were up a galloping 2% YOY. Even wages are not accelerating, let alone prices.

**Why The Married Lady Story?**

What do employers and employees really want from the economy? They want to make money, lots of it. Call it base gratification, if you will.

The Feldsteins of the world say there is a higher virtue that should be honored in the marketplace: that of zero inflation.

Feldstein is the married lady of macroeconomics.

**Democracy**

Let me pose this question: In a modern democracy, how will voters feel about free enterprise and capitalism if there are chronic “tight” labor markets?

How will voters feel if there is chronically high unemployment and weak labor markets and stagnant wages?

The Feldsteins of the world may wish to ponder the question.

Because a marriage should be about mutual gratification.

The “scene” that Feldstein supposedly is looking at:

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…Look, I said, I’m a born pessimist. For the sake of argument, let’s assume a worst case or nearly worst-case scenario for Europe. I don’t believe the euro zone can survive in its current form, and I think

Europe. What would the impact of that be on India, China, and all the other developing countries, particularly in Africa, whose trade is rapidly expanding with developing world’s two giants?is in for a deep recession, not a short shallow oneForget what the response on the panel was. It was unremarkable. What’s interesting is what happened later, during a coffee break, when I got into a discussion with two senior German executives attending the meeting.

The nature of these meetings is that the hallway chatter is always more interesting that the formal program. Part of the reason why is that, particularly when talking to journalists, the businesspeople or politicians tend to regard those conversations as off the record. So I’ll abide by that here. One of the German execs was a consultant, and the other headed what I’ll call a quasi-official German organization.

They were slightly irritated by the pessimism I’d expressed earlier in the day. “Don’t you realize,” one of them said, “that the cost to us (Germany) of bailing out Greece is far less than it cost us to reintegrate East Germany after the wall came down in 1989?”

I almost choked on my croissant. Yes, I replied, I am aware of that. I lived and worked in Berlin as a journalist in the mid 1990s, when that very painful (economically speaking) process was taking place in Germany. But doesn’t that, I said politely, rather beg the question: Germany integrating their brethren, who’d been isolated and impoverished during the cold war, was a dream come true, whatever the cost.

Germans, on the other hand paying to bail out Greece is, to average German, rather the opposite of a dream come true, is it not?He waved me off. No no, he said, it will be taken care of.

The Germans, he said, understood how beneficial to them membership in the euro zone has been. Without it, the gentleman said, the value of the Deutschemark would be 50% or 75% higher than it is under the euro. “German industry would be wiped off the map.”

Here was my ‘choking on my croissant’ moment number two. Most economists would agree with what my friend at the meeting had said; but he seemed either oblivious (not likely) or

(more likely) with thesimply unconcernedof what he had just uttered. Italy, to take the third-largest economy in Europe, one with a sizeable and modern industrial base, is stuck with a currency — the euro — which is stronger than the old lira would be under current circumstances. But membership in the euro zone means Italy can’t devalue to bring some relief to its exporters.flip sideI pushed back politely. Look, I said, it’s not Greece I’m worried about. It’s Italy. Third-biggest bond market in the world. Bond spreads this morning again heading over 7%(before the ECB intervened this to push them back down again.) Too big to fail, too big to save. Is the government, even one under a new Prime Minister

, going to push through sufficient austerity to avoid a default?Now the consultant perked up, speaking what he too believes to be the unvarnished truth.

, he said, because “They have toto be blunt about it, we have them [both the Greeks and the Italians] by the balls.”

Apparently, it´s not exactly working out that way!

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In fact, given that this was the 6^{th} year of recovery employment report, it was dismal! One pointer, if the participation rate had not dropped 0.2 points the unemployment rate, instead of falling to 5.3%, would have climbed to 5.7%.

No mystery that despite the “low” unemployment rate, wages stayed put, and remained at their 2% line year over year. Given that the “eager beavers” are watching wage growth with “hawk-eyes”, they must feel “depressed”!

In his preview of the Employment Report yesterday, Tim Duy concluded:

Bottom Line: Incoming data continues to support the case that the underlying pace of activity is holding, alleviating concerns that kept the Fed on the sidelines in the first half of this year. I anticipate the employment report, or, more accurately, the sum of the next three reports, to say the same.

, while Greece could push any rate hike beyond 2015. I myself, however, tend to be optimistic the Greece situation will not spiral out of control.Accelerating wage growth could very well be the trigger for a September rate hike

Seems he´s optimistic about everything, forgetting someone took out the “firing pin”. Shortly he´ll be talking December 15…March 16…

It was mind-boggling to hear this conclusion in Ed Lazear´s (a former CEA president) interview about the jobs report:

Interviewer: The numbers we have do not correlate with the zero interest rate policy. If you were at the Fed…

Ed: The numbers don’t give reason to raise interest rates but there´s no reason to keep rates low because that´s not helping the economy very much.

Uau!

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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 (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. 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.

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

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.

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

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.).

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

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.

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The Euro

“At the close of the “American century,” the euro has appeared as a potential rival, the countervailing power, to the dollar. *The advent of the euro may turn out to be the most important development in international monetary arrangements since the emergence of the dollar as the dominant currency shortly after the creation of the US central bank, the Federal Reserve System, in 1913.”*

“The drive for the Euro has been motivated by politics not economics. The aim has been to link Germany and France so closely as to make a future European war impossible, and to set the stage for a federal United States of Europe. I believe that adoption of the Euro would have the opposite effect. *It would exacerbate political tensions by converting divergent shocks that could have been readily accommodated by exchange rate changes into divisive political issues. Political unity can pave the way for monetary unity. Monetary unity imposed under unfavorable conditions will prove a barrier to the achievement of political unity.”*

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Yes:

A No vote would bring a new economic darkness. There is widespread agreement that the initial period would be characterised by default on Greece’s obligations to creditors, a chronic liquidity contraction and a solvency crisis in the banking sector, which would keep the banks shut. It would see a sclerotic blockage of most forms of economic activity. A further sharp GDP contraction would ensue. Whether or not the government chose to introduce a parallel currency to pay wages, pensions and other bills in the interim, a “new drachma” would be introduced. The currency would almost certainly drop sharply, most likely by about 50 per cent at first. Behind the wall of capital controls, the Bank of Greece would then print money. The risk of Greek deflation would disappear at a stroke. Banks would re-open, supported by the central bank and by a government programme to recapitalise them.

So Syriza would finally have re-taken control of Greece’s economic destiny.

.But it is unlikely to be successful in delivering a bright economic future, without help, for at least three reasons

No:

This Sunday, the Greek people will finally face a decisive choice, yay or nay, to stay in the eurozone. In the humble opinion of this writer, the Greeks should reject Europe’s terms, ditch the euro, and take their chances restarting their own currency.

I’m certainly not the first or the smartest person to recommend this course. But there’s an extra wrinkle to add: Along with its own self-preservation, Greece should do it for the sake of its fellow European nations, since a Grexit

might just shock Europe out of its crazed economic murder-suicide pact.

Images of Greece & Others

Contrast this chart

With this

Here Greece doesn´t standout at all, it´s super boom Ireland!

But Greece notches the biggest drop from the peak

Dives just as deep but stays there for longer than the US during the Great Depression

Comparing the “heathens” along “sacred” dimensions

Except for the pre-crisis debt level, no great (and unsurmountable) differences

Which leads me to endorse David Beckworth´s argument in The Monetary Origins of the Eurozone Crisis;

The Eurozone crisis is one of the greatest economic tragedies of the past century. It has caused immense human suffering and continues to this day. The standard view attributes it to a pre-crisis buildup of public and private debt augmented by the imposition of austerity during the crisis. While there is evidence of a relationship between these developments and economic growth during the crisis,

. In particular, the ECB’s tightening of monetary policy in 2008 and 2010-2011 seem to have not only caused two recessionsthis evidence upon closer examination points to the common monetary policy shared by these countries as the real culprit for the sharp decline in economic activity. This finding points to the need for a new monetary policy regime in the Eurozone. The case is made that the new regime should be a growth path target for total money spending.but sparked the sovereign debt crisis and gave teeth to the austerity programs

The illustrative pictures

Bottom Line: Greece, more than the rest had (has) enormous structural issues, but the Gordian knot of monetary policy only helped strangle it!

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The Federal Reserve must end its “excessively easy monetary policy [that] can no longer achieve a sustained increase in employment.”

So says (again) Martin Feldstein, renowned Harvard econ prof, old Reaganaut, writing on June 29 for the Project Syndicate.

Of course, Feldstein has been soap-boxing an inflationary doomsday since at least April 19 of 2009. Writing for the *Financial Times,* under the banner *Inflation Is Looming On America’s Horizon*, Feldstein said then only lower commodity prices were keeping inflation at bay, and stripping food and energy, that the CPI was already at 1.8%. “That is the good news: the outlook for the longer term is more ominous,” warned Feldstein.

The Fed was monetizing federal deficits, observed Feldstein, who literally concluded, “It is surprising that the long-term interest rates do not yet reflect the resulting risk of future inflation.”

We can hope Feldstein did not follow his own investment advice. In 2009, or all the subsequent years in which he has constantly rung the inflation klaxons.

**And Now?**

Evidently having given up on the QE-scaremongering, Feldstein now is running with a tight-labor markets argument. Rising wages will mean higher prices.

And indeed, average hourly earnings in May were up 2.3% YOY, and productivity has been weak. However, Feldstein ignores that for seven years, unit labor costs have been nearly dead in the water. From 2007 to 2015, unit labor costs are up about 7%, or less than 1% a year.

So, any increase in productivity going forward will tend to counteract higher wages, as has happened in the past. Really, a 2.3% annual wage increase is a reason for the monetary noose?

**An Interesting Question**

Suppose that the United States develops tighter labor markets, and official unemployment rates shrink.

In the 1990s, inflation ran between 4% and 1.5%, generally sinking as the decade went on. The unemployment rate shrank *also*, finishing the decade at 4.2%, well below the current 5.5% rate. So, based on recent history, the U.S. may not see that much of a budge in inflation.

But even if the U.S. did see some inflation—would it be a calamity to have tight labor markets and, say, steady 4% inflation? I mean, to anyone except central bankers and inflation-mongers?

How would the voters feel about free markets and capitalism if the U.S. had sustained tight labor markets and constant real wage growth? Or, conversely, lots of unemployment and wage stagnation?

Dudes, like I always say, print more money. When it is boom times in Fat City, voters will love making money the American way.

Feldstein made good, if right-wing PC, suggestions for structural reforms of labor markets. Sure, bring ‘em on. But the Fed should print lots of money too.

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What I am going to do next is to construct three bivariate Vector Auto-Regression (VAR) models to generate Impulse Response Functions (IRFs) in order to show what a shock to the monetary base leads to in terms of the price level and output. As mentioned in Part 1, the order of integration for the log levels of all four of our series (SBASENS, CPI, PCEPI and INDPRO) is one. With two unit roots per model, we are faced with a procedure that could lead to a VAR model in differences (a VARD), a VAR model in levels (a VARL), or a Vector Error Correction Model (a VECM).

Using the Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests I find that the order of integration is zero for all four series after they are differenced (as expected). In order to render the IRFs easier to interpret, for the rest of this analysis I have multiplied the natural log of each series by 100.

Since there is no evidence of cointegration between the monetary base and CPI or PCEPI, we are really only faced with a choice between a VARD and a VARL in these two cases. This means we are confronted with a tradeoff between statistical efficiency and the potential loss of information that takes place when time series are differenced. In the interests of thoroughness, I am going to do it both ways.

First, let’s estimate the VARDs. Most information criteria suggest a maximum lag length of one in both VARDs. The 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 three in both of these VARDs. The AR roots tables suggest that both VARDs are dynamically stable at this lag length.

Motivated by the dominant practice in the empirical literature on the transmission of monetary policy shocks, I am going to use a recursive identification strategy (Choleskey decomposition). Such a strategy means that the order of the variables affects the results. I will follow the traditional practice of ordering output and the price level before the monetary policy instrument in each vector. The response standard errors I will show are analytic, as Monte Carlo standard errors change each time an IRF is generated.

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

And here are responses to a shock to the monetary base in the VARD including PCEPI as a variable.

In each case 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 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 estimate the VARLs. Most information criteria suggest a maximum lag length of two in both VARLs. The 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 three in both of these VARLs. 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 VARL including CPI as a variable. In this case I’ll extent the time period to 48 months.

And here are responses to a shock to the monetary base in the VARL including PCEPI as a variable.

A positive shock to the monetary base generates a statistically significant positive response to the CPI in months three and four. A positive shock to the monetary base generates a statistically significant positive response to the PCEPI in months two through five. Changing the impulse definition to Generalized Impulse renders the responses statistically insignificant (there is little difference using Residual impulses), but we’ve already established that the monetary base has a statistically significant positive effect on CPI and PCEPI with the VARDs. And, as I said earlier, there is loss in statistical efficiency when estimating a VARL with unit roots.

The IRFs show that a 2.5% and 2.6% shock to the monetary base in month one leads to a peak increase in the CPI level of 0.12% and in the PCEPI level of 0.085% in month four respectively. In short, the empirical evidence does not seem to be very supportive of the Neo-Fisherite hypothesis.

Now let us turn our attention to industrial production.

In Part 1 we showed that there is evidence of cointegration between the monetary base and industrial production. This means, in addition to the option of estimating a VARD or a VARL, we may also estimate a VECM. But before discussing the pros and cons of doing this, let us estimate a VARD and VARL first. I should also mention at this point that, in a book edited by David Glasner, “Business Cycles and Depressions: An Encyclopedia”, Neil Ericsson (in an article entitled “Distributed Lags”) argues that estimating a model in first differences alone when cointegration exists discards the information contained in the levels and leads to model misspecification. Consequently a VARL is probably preferred to a VARD in this case, but it may still be useful to estimate both.

First let’s estimate the VARD. Most information criteria suggest a maximum lag length of three in the VARD. The LM test suggests that there is 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 is the IRF for the VARD.

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. Changing the impulse definition to Residual or Generalized Impulse doesn’t change the results much, if at all.

Now, let’s estimate the VARL. Most information criteria suggest a maximum lag length of four in the VARL. The LM test suggests that there is no problem with serial correlation at this lag length. The AR roots tables suggests that the VARL is dynamically stable at this lag length. Here is the IRF for the VARL.

A positive shock to the monetary base generates a statistically significant negative response to level of industrial production in the third month, followed by a statistically significant positive response in months eight through 17. Changing the impulse definition to Residual doesn’t change the results much, if at all. Changing the impulse definition to Generalized Impulse ** eliminates** the statistically negative response in the third month.

The IRF shows that a 2.5% shock to the monetary base in month one leads to a peak increase in industrial production of 0.43% in month 13.

Now, let’s talk about the pros and cons of estimating a VECM. The advantage of a VECM is that it can generate statistically efficient estimates without losing long-run relationships among the variables. Thus, if cointegration exists, and the true cointegrating relationship is known and can be given a theoretical interpretation, it’s generally acknowledged that a VECM should be estimated in the manner suggested by Johansen (1995).

On the other hand, if the true integrating relationship is unknown, imposing cointegration may not be appropriate. Imposing incorrect cointegrating relationships can lead to biased estimates and hence bias the IRFs derived from the VARL. 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. Moreover, Sims et al. (1990) show that when a cointegrating relationship exists, the systems dynamics can be estimated consistently with a VARL, and James Hamilton (1994) appears to agree (pp. 651-653). As a final note on the pros and cons of VARDS, VARLS and VECMs when modeling and forecasting with cointegrated variables, I highly recommend this “hands-on” paper by Tim Duy and Mark Thoma.

Nevertheless, I think it will still be interesting to estimate a VECM for industrial production. The following IRF is generated assuming a linear trend in the data and an intercept but no trend in the cointegrating vector. (Unfortunately VECM standard errors are not available in EViews.).

A positive shock to the monetary base generates a negative response to level of industrial production in the second and third month, followed by a positive response thereafter. A 2.4% shock to the monetary base in month one leads to a peak increase in industrial production of 0.51% in month 15. In this model the response of industrial production is remarkably persistent with the level of industrial production still up by 0.43% nearly four years later. Changing the impulse definition (to either Residual or Generalized Impulse) slightly ** increases **the response. In any case, as I’ve already implied, I don’t put much stock in this VECM.

Here are a couple of preliminary observations. The price level responses seem less persistent than what multivariable VARs estimated in “normal” times with short term interest rates as the instrument of monetary policy show. On the other hand, the output response seems somewhat more persistent.

In Part 3 I shall finally put output, the price level and the monetary base together in our baseline trivariate VAR model.

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Most highly publicized academic studies on quantitative easing (QE) seem to come in one of four flavors: 1) event studies on changes in security yields on the days of announcement (e.g. Krishnamurthy and Vissing-Jorgensen, 2011), 2) panel data studies on flow and stock effects of QE on daily security yields during the programs (e.g. D’Amico and King, 2010) , 3) times series studies on the effect of open market operations on security yields during normal times (e.g. Hamilton and Wu, 2011) and 4) studies on the macroeconomic effects of QE using major models calibrated to normal times (e.g. Fuhrer and Olivei 2011). The underlying assumption of nearly all these studies is that the primary channel of the Monetary Transmission Mechanism (MTM) is the Traditional Real Interest Rate Channel, which is almost certainly not the case at the zero lower bound (ZLB) in interest rates.

Notably, there are very few empirical studies on the macroeconomic effects of QE ** during** QE. Indeed, to my knowledge, there are only four: Honda

What these four studies have in common is that they focus on periods of zero interest rate policy (ZIRP) employing Vector Auto-Regression (VAR) methodology with the monetary base, or bank reserves, as the instrument of monetary policy. The convention in the empirical literature on the transmission of monetary policy is to estimate a VAR with a measure of output, the price level and a short term interest rate (along with other variables). Thus, the principal difference between these four studies, and what is the usual practice, is to substitute the monetary base (or bank reserves) in place of the short term interest rate as the instrument of monetary policy.

Focusing on periods of ZIRP also presents some additional challenges. In particular, instead of having decades of data permitting the use of real GDP (RGDP) and the GDP deflator as the measure of output and price level, there is only a period of years usually necessitating the use of data at monthly frequency, meaning (for example) that the industrial production index may have to be substituted for RGDP, and that a measure of the consumer price level may have to be substituted for the GDP deflator, if a sufficient number of observations is to be available in order for it to be possible to generate statistically significant results.

When constructing a macroeconomic VAR model (as I am about to do), it is especially desirable for the policy variable to Granger cause another variable (or variables) in the model. This is because, if the policy variable Granger causes another variable, then it provides statistically significant information about future values of the other variable. Under those circumstances we might expect shocks to the policy variable in the VAR model to lead to statistically significant changes in the other variable.

To that end, let us consider the relationship between the St. Louis Source Base (SBASENS) and the Consumer Price Index (CPI), the Personal Consumption Expenditures Price Index (PCEPI) and the Industrial Production Index (INDPRO). Here is the natural log of SBASENS and CPI:

the natural log of SBASENS and PCEPI:

and the natural log of SBASENS and INDPRO from December 2008 through May 2015:

The following analysis is performed using a techniques developed by Toda and Yamamato (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 four series. I set up three 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 pair of VARs that include the price level as a variable. The 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 three in both of these VARs. The AR roots tables suggest that both VARs are dynamically stable at this lag length, and Johansen’s Trace Test and Maximum Eigenvalue Test both indicate the two pairs of series are not cointegrated at this lag length.

Most information criteria suggest a maximum lag length of four for the VAR that includes the industrial production index as a variable. The LM test suggests that there is no problem with serial correlation. 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 industrial production.

Then I re-estimated the three 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, 1 to 4, and 1 to 5 respectively, I left the intervals at 1 to 3, 1 to 3, and 1 to 4, 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 reject the null that CPI does not Granger cause the monetary base at the 5% significance level, and I reject the null that monetary base does not Granger cause CPI at the 1% significance level.
- I reject the null that PCEPI does not Granger cause monetary base at the 5% significance level, and I reject the null that monetary base does not Granger cause PCEPI at the 1% significance level.
- I reject the null that industrial production does not Granger cause the monetary base at the 5% significance level, and I reject the null that monetary base does not Granger cause industrial production at the 1% significance level.

In other words, there is strong evidence of bidirectional Granger causality between the monetary base and CPI, PCEPI and industrial production from December 2008 through May 2015. Moreover the evidence for Granger causality from the monetary base to CPI, PCEPI and industrial production is slightly stronger than the evidence for Granger causality from CPI, PCEPI and Industrial production to the monetary base.

The next step in this process is to determine the nature of this “correlation”. What does a shock to the monetary base lead to in terms of the price level and output? For example, does a positive shock to the monetary base cause the price level to decline (counterfactually) as the Neo-Fisherites seem to be claiming?

Or might it cause the price level to increase (counterfactually) as Monetarists claim? And what happens to output? In order to determine this we need to estimate properly specified VARs, and then to generate the appropriate Impulse Response Functions (IRFs).

For that, tune in next time.

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