# QE and Business Investment: The VAR Evidence: Part 3

What we are 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 inflation expectations, stock prices and the value of the US dollar leads to in terms of business investment. As mentioned in Part 2, all four of our series (T5YIEM, DJIA, TWEXBPA and ANXAVS) have unit roots. With unit roots in our models, 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).

Since there is no evidence of cointegration between investment in equipment and stock prices or the value of the US dollar, we are really only faced with a choice between a VARD and a VARL in these two cases. And although the existence of cointegration between investment in equipment and inflation expectations means that a VECM is an option in the third case, given the pros and cons of doing so, I am not going to estimate a VECM. For a detailed discussion of what these pros and cons are, see this post.

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. As we shall soon see, this is not at all an issue, so in the interests of brevity, I am only going to estimate three VARLs.

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 (Cholesky decomposition). Such a strategy means that the order of the variables affects the results. I will follow the traditional practice of ordering the goods and services market variables before the financial market variables in each vector. The response standard errors I will show are analytic, as Monte Carlo standard errors change each time an IRF is generated. In order to render the IRFs easier to interpret, for the rest of this analysis, with the exception of T5YIEM (which is already in percent) I have multiplied the log level of each series by 100.

Let’s look at the effect of a positive shock to inflation expectations first.

Most information criteria suggest a maximum lag length of two in the VAR involving inflation expectations. The LM test suggests that there is no problem with serial correlation at this lag length. The AR roots tables suggest that the VAR is dynamically stable at this lag length. Here are the responses to a shock to inflation expectations.

A positive shock to inflation expectations leads to a statistically significant positive response to investment in equipment in months two through 31, or a period lasting nearly two and a half years. The IRFs show that a 13 basis point shock to inflation expectation in month one leads to a peak increase in investment in equipment of 1.04% in month 11. Recall that we previously showed that a positive 2.6% shock to the monetary base (QE) leads to an increase in inflation expectations of 4.8 basis points.

Now let’s look at the effect of a positive shock to stock prices.

Most information criteria suggest a maximum lag length of one in the VAR involving stock prices. The LM test suggests that there is no problem with serial correlation at this lag length. The AR roots tables suggest that the VAR is dynamically stable at this lag length. Here are the responses to a shock to stock prices.

A positive shock to stock prices leads to a statistically significant positive response to investment in equipment in months two through 40, or a period lasting over three years. The IRFs show that a 3.1% shock to stock prices in month one leads to a peak increase in investment in equipment of 1.10% in month 15. Recall that we previously showed that a positive 2.3% shock to the monetary base (QE) leads to an increase in stock prices (DJIA) of 1.6%.

Finally let’s look at the effect of a negative shock to the value of the US dollar.

Most information criteria suggest a maximum lag length of four in the VAR involving the US dollar. The LM test suggests that there is no problem with serial correlation at this lag length. The AR roots tables suggest that the VAR is dynamically stable at this lag length. 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 make the IRFs easier to interpret. Here are the responses to a shock to the value of the US dollar.

A positive shock to the value of foreign currency in month one leads (with the sole exception of month 5) to a statistically significant positive response in investment in equipment in months three through 27, or a period lasting over two years. The IRFs show that a 0.90% shock to the value of foreign currency in month one leads to a peak increase in investment in equipment of 1.16% in month 25. Recall that we previously showed here and here that a positive 1.9-2.5% shock to the monetary base (QE) leads to an increase in the value of the euro (1.5%), the Canadian dollar (1.4%), the Mexican peso (1.1%) and the Japanese yen (1.1%) in terms of the US dollar.

Now that we’ve established the empirical facts concerning QE and investment in equipment, let’s discuss the monetary theory that explains these facts.

As we have previously discussed, a positive shock to the US monetary base increases expected Nominal GDP (NGDP), or expected aggregate demand (AD). Higher expected AD means higher inflation expectations, ceteris paribus. Higher expected AD also leads to higher nominal stock prices. And higher expected inflation leads to an increase in the expected real exchange rates of foreign currencies in terms of the US dollar.

So why do higher inflation expectations, higher stock prices and a lower US dollar lead to increased investment in equipment?

Inflation expectations are the closest proxy we have for expected NGDP as an increase in expected NGDP should lead to an increase in inflation expectations, ceteris paribus. An increase in expected NGDP should lead to an increase in investment in equipment as businesses anticipate rising sales and increased profit making opportunities.

James Tobin’s q theory provides a mechanism through which increased NGDP expectations lead to increased investment in equipment 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 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 they are buying. Thus investment spending will rise because corporations can purchase new equipment with only a small issue of stock.

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 if US goods and services become more competitive with goods and services priced in foreign currencies, this provides an incentive for US businesses to increase their investment in equipment.

And what of Robert Waldmann’s theoretical argument that QE leads to less business investment by raising the price of long term Treasuries (lowering their yields)?

The biggest problem with this theory is the empirical fact, despite the widely accepted myth otherwise, that QE leads to higher bond yields.

In Waldmann’s defense, he states that he is sure that Michael Spence and Kevin Warsh are wrong, and that he is simply making a theoretical argument for their conclusion, something which DeLong and Krugman argued Spence and Warsh had failed to do.

And, something which I hitherto have not discussed, just how important is the equipment component of business investment?

The three main components of private nonresidential fixed investment (PNFI) are 1) equipment, 2) intellectual property rights, and 3) structures. In the US in 2014 PNFI totaled \$2,233.7 billion. Equipment represented \$1036.7 billion of that total or 46.4%. Intellectual property rights (software, R&D and artistic rights) represented \$690 billion of that total or 30.9%.  Structures represented \$507 billion of that total or 22.7%.

Thus equipment is by far the most important component of business investment, and I find it remarkably difficult to believe, given QE’s demonstrably positive effect on investment in equipment (as well as its demonstrably positive effect on the output and price level), that it might have a negative effect on business investment overall.

# QE and Business Investment: The VAR Evidence: Part 2

In Part 1 we demonstrated that Value of Manufacturers’ Shipments for Capital Goods: Nondefense Capital Goods Excluding Aircraft Industries (ANXAVS) is a monthly frequency proxy for private nonresidential investment in equipment.

In Part 2 we are going to check if inflation expectations, stock prices and the value of the US dollar are correlated with private nonresidential investment in equipment in the Age of Zero Interest Rate Policy (ZIRP). Specifically we’re going to check if the 5-Year Breakeven Inflation Rate (T5YIEM), Dow Jones Industrial Average (DJIA) and the Real Trade Weighted U.S. Dollar Index: Broad (TWEXBPA) each Granger cause ANXAVS. This analysis is performed using a technique developed by Toda and Yamamoto (1995).

First let’s consider inflation expectations. Here is T5YIEM and the natural log of ANXAVS from December 2008 through September 2015.

Using the Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests I find that the order of integration is one for T5YIEM and two for LANXAVS. I set up a two-equation Vector Auto-Regression (VAR) in the levels of the data including an intercept for each equation.

Most information criteria suggest a maximum lag length of two. The LM test suggests that there is no problem with serial correlation at this lag length. The AR roots tables suggest that the VAR is dynamically stable at this lag length, and Johansen’s Trace Test and Maximum Eigenvalue Test both indicate the series are cointegrated at this lag length. This suggests that there must be Granger causality in at least one direction between T5YIEM and ANXAVS.

Then I re-estimated the level VAR with two extra lags of each variable in each equation. But rather than declare the lag interval for the two endogenous variables to be from 1 to 4, I left the intervals at 1 to 2, and declared the extra two lags of each variable to be exogenous variables. Here are the Granger causality test results.

Thus, I fail to reject the null hypothesis that private nonresidential investment in equipment does not Granger cause inflation expectations, but I reject the null hypothesis that inflation expectations does not Granger cause private nonresidential investment in equipment at the 5% significance level. In other words there is evidence that inflation expectations Granger causes private nonresidential investment in equipment from December 2008 through September 2015, but not the other way around.

Next let’s consider stock prices. Here is the natural log of DJIA and ANXAVS from December 2008 through September 2015.

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

Most information criteria suggest a maximum lag length of one for the VAR. The 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 two extra lags 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 1, and declared the extra two lags of each variable to be exogenous variables. Here are the Granger causality test results.

Thus, I fail to reject the null hypothesis that private nonresidential investment in equipment does not Granger cause stock prices, but I reject the null hypothesis that stock prices does not Granger cause private nonresidential investment in equipment at the 10% significance level. In other words there is evidence that stock prices Granger causes private nonresidential investment in equipment from December 2008 through September 2015, but not the other way around.

Finally let’s consider the value of the US dollar. Here is the natural log of TWEXBPA and ANXAVS from December 2008 through September 2015.

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

Most information criteria suggest a maximum lag length of four for the VAR. The 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 two extra lags of each variable in each equation. But rather than declare the lag interval for the two endogenous variables to be from 1 to 6, I left the intervals at 1 to 4, and declared the extra two lags of each variable to be exogenous variables. Here are the Granger causality test results.

Thus, I fail to reject the null hypothesis that private nonresidential investment in equipment does not Granger cause the value of the US dollar, but I reject the null hypothesis that the value of the US dollar does not Granger cause private nonresidential investment in equipment at the 1% significance level. In other words there is evidence that the value of the US dollar Granger causes private nonresidential investment in equipment from December 2008 through September 2015, but not the other way around.

The next step in this process is to determine the nature of these “correlations”. What do positive shocks to inflation expectations, positive shocks to stock prices, and negative shocks to the value of the US dollar lead to in terms of private nonresidential investment in equipment? Do they lead to a decline in investment as Mike Spence and Kevin Warsh are implicitly claiming?

Or might they cause investment to increase (counterfactually) as Monetarists claim? In order to determine this we will estimate properly specified bivariate VARs and generate appropriate Impulse Response Functions (IRFs).

For that, tune in next time.

# Stephen Williamson Discovers VAR Analysis

In his most recent post Stephen Williamson states the following:

“The modern version of the Monetary History approach is VAR (vector autoregression) analysis. This preliminary version of Valerie Ramey’s chapter for the second Handbook of Monetary Economics is a nice survey of how VAR practitioners do their work. The VAR approach has been used for a long time to study the role of monetary factors in economic activity. If we take the VAR people at their word, the approach can be used to identify a monetary policy shock and trace its dynamic effects on macroeconomic variables – letting the data speak for itself, as it were…But, should we buy it? First, there are plenty of things to make us feel uncomfortable about VAR results with regard to monetary policy shocks. As is clear from Ramey’s paper, and to anyone who has read the VAR literature closely, results (both qualitative and quantitative) are sensitive to what variables we include in the VAR, and to various other aspects of the setup. Basically, it’s not clear we can believe the identifying assumptions…”

As Chris Sims (1996) noted in response to similar criticism of VAR by Glenn Rudebusch, issues of “variable selection are universal in macroeconomic modeling” (pp. 9). And as for the issue of identification, the Ramey paper to which Williamson links lists ten different approaches, all of which are associated with VAR modeling to some degree or another.

So what is the alternative to VAR modeling?

Presumably, from his later criticism of Christiano, Eichenbaum and Evan’s (2005) approach to DSGE modeling, which matches the impulse responses from the model to those of actual data, Williamson would prefer models achieve identification by imposing structure based on theory. But DSGE identification is even less straightforward than VAR identification. Canova and Sala (2009), Komunjer and Ng (2011), and others have pointed out some of the many problems with identification in DSGE models.

And, in the final analysis, this criticism of VAR on the basis of identification is ironic given it is no exaggeration to say that it was in fact the “incredible identification” of large scale models that was the primary motivation for Chris Sims (1980) to introduce VAR analysis to macroeconomics.

Williamson goes on to provide another objection to VAR modeling:

“…Second, even if you take VAR results at face value, the results will only capture the effect of an innovation in monetary policy. But, modern macroeconomics teaches us that this is not what we should actually be interested in. Instead, we should care about the operating characteristics of the economy under alternative well-specified policy rules. These are rules specifying the actions the central bank takes under all possible circumstances. For the Fed, actions would involve setting administered interest rates – principally the interest rate on reserves and the discount rate – and purchasing assets of particular types and maturities.”

I think the best response to this is to turn to page 24 of the Ramey paper which Williamson cites in his post:

”Before beginning, it is important to clarify why we are interested in monetary policy shocks. Because monetary policy is typically guided by a rule, most movements in monetary policy instruments are due to the systematic component of monetary policy rather than to deviations from that rule. Why, then, do we care about identifying shocks? We care about identifying shocks for a variety of reasons, the most important of which is to be able to estimate causal effects of money on macroeconomic variables. As Sims (1998) argued in his discussion of Rudebusch’s (1998) critique of standard VAR methods, because we are trying to identify structural parameters, we need instruments that shift key relationships. Analogous to the supply and demand framework where we need demand shift instruments to identify the parameters of the supply curve, in the monetary policy context we require monetary rule shift instruments to identify the response of the economy to monetary policy.”

Failure to correctly identify the effect of an innovation in monetary policy might for example allow us to theorize that raising interest rates causes inflation to increase.

Fortunately, partly thanks to VAR analysis, most economists don’t consider that to be very plausible (just as most people don’t think that it is the act of opening umbrellas that causes it to rain).

In comments Williamson says the following:

“In the quote, you can see roughly what Friedman and Schwartz were up to. They looked at turning points in money supply and turning points in what he calls “general business.” I haven’t read the Monetary History in a long time, but I think “general business” is the NBER “reference cycle,” which is roughly an index of aggregate economic activity – not aggregate output, but presumably highly correlated with it. Basically, Friedman and Schwartz showed that money leads aggregate economic activity. It’s the informal counterpart of what Sims (1972) is about. Sims showed that money Granger-causes output in the the U.S. time series. Of course Granger causation need not imply economic causation. That was part of Tobin’s critique of Friedman and Schwartz. Money could in fact be endogenously responding to output, but appear to lead output in the time series. The endogeneity could come from policy, or from the banking sector, if we’re measuring money as M1 or M2, say.”

Williamson is referring to Tobin’s famous Post Hoc, Proctor Hoc (“after this, therefore because of this”) critique of Friedman.

Williamson implies that Granger causality tests are subject to the very same criticism, when in fact Chris Sim’s 1972 paper was specifically intended as a rebuttal to Tobin’s invocation of the fallacy (which is incredibly clear if one actually bothers to read the paper). Williamson’s comment on the endogeneity of money is even more ironic when one realizes that Granger causality testing is the primary econometric tool of the Post Keynesian empirical literature on endogenous money (e.g. Basil Moore, Thomas Palley, Robert Pollin, Peter Howells etc.).

# Fiscal and Monetary Policy Interaction during the Age of ZIRP: Part 3

In Part 3 we will add general government consumption and investment and general government net taxes to the trivariate baseline Vector Auto-Regression (VAR). Parts 1 and 2 can be found here and here.

With Government Wage and Salary Disbursements and Total Public Construction Spending (GWSDTPC) and Net Personal Taxes (monthly frequency proxies for general government consumption and investment and general government net taxes respectively) added to the baseline VAR model, most information criteria suggest a maximum lag length of four. The 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 two cointegrating equation at this lag length. But this is expected, since we have evidence that the the monetary base is cointegrated with industrial production, and that net personal taxes is cointegrated with both PCEPI and industrial production. 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 (Cholesky decomposition). Such a strategy means that the order of the variables affects the results. I will follow the practice of Fatas and Mihov (2001) in ordering general government consumption and investment spending first, the output level second, the price level third, general government net tax revenue fourth and the monetary policy instrument last.

This ordering assumes that government consumption and investment spending is not affected contemporaneously by shocks originating in other sectors of the economy, and that changes in government consumption and investment spending, unlike changes in net tax revenue, are largely unrelated to the business cycle. Ordering the output level and the price level before net tax revenue can be justified on the grounds that shocks to these two variables have an immediate impact on the tax base and, thus, a contemporaneous effect on net tax revenue.

Thus this ordering of variables captures the effects of automatic stabilizers on net tax revenue. This ordering also 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.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 of the output level and the price level to government spending, net taxes and the monetary base in the five-variable VAR.

The response of the level of industrial production and the price level to a positive shock to general government consumption and investment spending is statistically insignificant in every month. Similarly, the response of the level of industrial production and the price level to a positive shock to general government net tax revenue is statistically insignificant in every month.

In contrast, a positive shock to the monetary base in month one leads to a statistically significant positive response in the level of industrial production in months five through 12. Furthermore, a positive shock to the monetary base in month one leads to a statistically significant positive response in the price level in month three.

The IRFs show that a positive 2.1% shock to the monetary base in month one (first line above) leads to a peak increase in the level of industrial production of 0.19% in month ten (second line above). They also show that a positive 2.1% shock to the monetary base in month one (second line) leads to a peak increase in the price level of 0.050% in month three (first line).

The bottom line is that there is no evidence that general government consumption and investment spending and general government net tax changes have had a statistically significant effect on either the output level or the price level from December 2008 through May 2015, or during the Age of Zero Interest Rate Policy (ZIRP). This is consistent with the Granger causality and bivariate VAR evidence presented in Part 2. On the other hand there is evidence that monetary base changes have had a statistically significant effect on both the output level and the price level in the Age of ZIRP. This is consistent with the evidence which I presented in the twelve part series on the Monetary Base and the Channels of Monetary Transmission which concluded here.

Since we can conclude that fiscal policy has had no statistically significant effect on the output level or the price level in the Age of ZIRP, and that monetary policy has, it might be useful to investigate the effect that fiscal policy changes have had on monetary policy. Here are the responses of the government spending, net taxes and the monetary base to each other in the five-variable VAR.

The response of the monetary base to a positive shock to general government consumption and investment spending is statistically insignificant in every month. However, the response of the monetary base to a positive shock to general government net tax revenue is statistically significant in months three through eight. The IRFs show that a positive 4.0% shock to general government net tax revenue in month one leads to a peak increase in the monetary base of 1.7% in month six.

In other words, there is evidence that general government net tax changes have had a statistically significant effect on the monetary base in the Age of ZIRP.

Given the events surrounding the implementation of QE3 in particular, this shouldn’t be too surprising.

In mid-2012, several FOMC members (e.g. Evans, Rosengren and Williams) specifically mentioned the then forthcoming “fiscal cliff” as a motivation for additional monetary stimulus. An increase in income tax rates applicable to high income tax payers, and an increase in payroll taxes went into effect on January 1, 2013. These tax increases constituted approximately 70% of the budgetary effect of going over the “cliff” and are clearly visible in the graph of Net Personal Taxes in Part 2 of this post.

Between April 2012 and April 2013, Net Personal Taxes increased from \$726.5 billion to \$1,021.0 billion at an annual rate, a staggering 40.5% increase year-on-year. Given the above elasticity, and the five month lag to peak effect, this suggests that a substantial proportion of the increase in the monetary base under QE3 from September 2012 to September 2013 was in response to the fiscal cliff tax increase.

As Scott Sumner pointed out, recent estimates of Real GDP (RGDP) growth rates, Q4 over Q4, show that RGDP growth was only 1.7% and 1.3% in 2011 and 2012 respectively, before QE3 and the fiscal cliff, and was a more substantial 2.45% and 2.525% in 2013 and 2014, after QE3 and the fiscal cliff. It’s not hard to draw a connection between the improvement in RGDP growth rates after QE3 and the fiscal cliff and the VAR evidence that net tax changes have had no statistically significant effect on either the output level or the price level, that positive monetary base changes have had a statistically significant positive effect on both the output level and the price level, and that positive net tax changes have had a statistically significant positive effect on monetary base changes.

And the slow RGDP growth in 2011 and 2012 can itself be connected to this phenomenon.

Prior to the fiscal cliff, the largest discretionary changes in net taxes were those implemented as part of the “fiscal stimulus”. According to BEA estimates (via FRED), between 2008Q4 and 2010Q1, due to the American Reinvestment and Recovery Act (ARRA) Federal personal current taxes were reduced by \$130.9 billion at an annual rate, and refundable tax credits to persons were increased by \$29.7 billion at an annual rate. Thus Net Personal Taxes were reduced by \$160.6 billion at an annual rate. This persisted through 2010Q4, and most of this reduction in Net Personal Taxes was maintained in the form of the 2% “payroll tax holiday” until the advent of the 2013 fiscal cliff.

The \$160.6 billion discretionary cut in Net Personal Taxes meant that Net Personal Tax revenue was only \$444.1 billion in March 2010, instead of \$604.7 billion, a reduction of 26.6%. March 2010 also happened to be the month that QE1 was concluded. Thus the VAR estimates suggest that QE1 was probably substantially smaller in response to the cut in Net Personal Taxes enacted under the 2009 fiscal stimulus.

I suspect that the FOMC had expected a much larger economic response to the tax changes than actually occurred in 2010, and this is the main reason why they grudgingly acquiesced to the ad hoc \$600 billion in monetary stimulus under QE2. It wasn’t until the specter of the 2013 fiscal cliff that a substantial amount of open ended quantitative easing was finally unleashed, and in turn it wasn’t until this act that RGDP growth was anything other than pathetically stagnant during the recovery from the Great Recession.

The upshot of all this is that the FOMC has behaved as though taxes have a substantial fiscal multiplier. They have reacted to tax cuts by reducing monetary stimulus, and to tax increases by increasing monetary stimulus. Since the time series econometric evidence shows that the tax cut multiplier is not statistically different from zero, and that quantitative easing has statistically significant effects on the output level and the price level, this means that tax cuts have had the perverse effect of leading to less economic growth and, similarly, that tax increases have led to increased economic growth.

Thus, in the Age of ZIRP, the monetary offset of fiscal policy has effectively meant that the fiscal multiplier has not only been zero, it has been negative.

# Fiscal and Monetary Policy Interaction during the Age of ZIRP: Part 2

In Part 1 we demonstrated that Government Wage and Salary Disbursements and Total Public Construction Spending (GWSDTPC) and Net Personal Taxes are monthly frequency proxies for   general government consumption and investment and general government net taxes respectively.

In Part 2 we are going to check if general government consumption and investment and general government net taxes are correlated with the output level or the price level in the Age of Zero Interest Rate Policy (ZIRP). Specifically we are going to check if GWSDTPC and Net Personal Taxes each Granger cause the Personal Consumption Expenditures Price Index (PCEPI) or industrial production (INDPRO). This analysis is performed using a techniques developed by Toda and Yamamoto (1995).

First let’s consider GWSDTPC. Here is the natural log of GWSDTPC and PCEPI, and the natural log of GWSDTPC and INDPRO from December 2008 through May 2015.

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 Vector Auto-Regressions (VARs) in the log levels of the data including an intercept for each equation.

Most information criteria suggest a maximum lag length of one for the VAR involving PCEPI. The LM test suggests that there is no problem with serial correlation at this lag length. The AR roots tables suggest that the VAR is dynamically stable at this lag length, and Johansen’s Trace Test and Maximum Eigenvalue Test both indicate the series are not cointegrated at this lag length.

Most information criteria suggest a maximum lag length of one for the VAR involving INDPRO. The 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. This might be a problem if our primary objective in estimating the bivariate VAR was to look at its impulse response functions (IRFs). Fortunately, the Granger causality test results do not rely on the bivariate VAR being dynamically stable. The Johansen’s Trace Test and Maximum Eigenvalue Test both indicate 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 2, I left the intervals at 1 to 1, and declared the extra lag of each variable to be exogenous variables. Here are the Granger causality test results.

Thus, the results are as follows:

• I fail to reject the null hypothesis that the price level does not Granger cause general government consumption and investment, and I fail to reject the null hypothesis that general government consumption and investment does not Granger cause the price level.
• I fail to reject the null hypothesis that industrial production does not Granger cause general government consumption and investment, and I fail to reject the null hypothesis that general government consumption and investment does not Granger cause industrial production.

In other words, there is no evidence of Granger causality in either direction between general government consumption and investment and the price level or industrial production from December 2008 through May 2015. Given that the number of covariates in each of these tests is only five, and that the number of included observations in each test is 76, the statistical power of these tests (i.e. the probability that the test correctly rejects the null hypothesis when the alternative hypothesis is true) is already quite high. It is unlikely that simply increasing the sample size would change these results.

Next let’s consider Net Personal Taxes. Here is the natural log of Net Personal Taxes and PCEPI, and the natural log of Net Personal Taxes and INDPRO from December 2008 through May 2015.

Using the Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests I find that the order of integration is three for Net Personal Taxes. 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 involving PCEPI. The LM test suggests that there is no problem with serial correlation at this lag length. The AR roots tables suggest that the VAR is dynamically stable at this lag length, and Johansen’s Trace Test and Maximum Eigenvalue Test both indicate the series are cointegrated at this lag length. This suggests that there must be Granger causality in at least one direction between the Net Personal Taxes and PCEPI.

Most information criteria suggest a maximum lag length of two for the VAR involving INDPRO. The 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. The Johansen’s Trace Test indicates the two series are cointegrated at this lag length, although the Maximum Eigenvalue Test does not.

The possible existence of cointegration suggests that there might be Granger causality in at least one direction between the Net Personal Taxes and INDPRO

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 5, I left the intervals at 1 to 2, and declared the extra three lags of each variable to be exogenous variables. Here are the Granger causality test results.

Thus, the results are as follows:

• I fail to reject the null hypothesis that the price level does not Granger cause general government net taxes, but I reject the null hypothesis that general government net taxes does not Granger cause the price level at the 10% significance level.
• I fail to reject the null hypothesis that industrial production does not Granger cause general government net taxes, but I reject the null hypothesis that general government net taxes does not Granger cause industrial production at the 5% significance level.

In other words there is evidence that general government net taxes Granger causes the price level and industrial production from December 2008 through May 2015, but not the other way around.

Since there is evidence of Granger causality from general government net taxes to the price level and to industrial production, I am next going to construct two bivariate VARs to generate Impulse Response Functions (IRFs) in order to show what a shock to taxes leads to in terms of the price level and output. Since the order of integration of Net Personal Taxes is three, statistical efficiency will be maximized if we estimate a VAR in differences (a VARD) with both series differenced three times.

Most information criteria suggest a maximum lag length of four in the VARD involving PCEPI. 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 five. The AR roots tables suggest that the VARD is dynamically stable at this lag length.

Most information criteria suggest a maximum lag length of six in the VARD involving INDPRO. The LM test suggests that there is no problem with serial correlation at this lag length. The AR roots tables suggest that the VARD is dynamically stable at this lag length.

I am using a recursive identification strategy (Cholesky decomposition). Such a strategy means that the order of the variables affects the results. I will follow the practice of Fatas and Mihov (2001) in ordering output and the price level before net taxes in each vector. The response standard errors I will show are analytic, as Monte Carlo standard errors change each time an IRF is generated.

A shock to general government net taxes fails to lead to a statistically significant response in prices or industrial production in any month. Changing the impulse definition to Residual or Generalized Impulse doesn’t change this result. So despite the fact that there is evidence of Granger causality from general government net taxes to the price level and to the output level, there is no evidence of a statistically significant effect of a shock to net taxes on either.

In Part 3 we will add general government consumption and investment and general government net taxes to the trivariate baseline VAR.

What is the effect of a shock to government spending or taxes on the economy in general? More importantly, what is the response of monetary policy to changes in fiscal policy?

Tune in next time and find out.

# Fiscal and Monetary Policy Interaction during the Age of ZIRP: Part 1

Having just developed the Simple Baseline Vector Auto-Regression (VAR) Model for Studying the US Monetary Base and the Channels of Monetary Transmission the logical next step is to examine the interaction of fiscal and monetary policy in the Age of Zero Interest Rate Policy (ZIRP).

Robert Hall (2009) provides a reasonably accessible summary of the time series econometric evidence concerning the effectiveness of fiscal policy with a special emphasis on the government purchases multiplier. The section on fiscal policy VAR studies can be found on pages 192 to 195.

Fiscal policy VAR identification approaches fall into four main categories: 1) the recursive approach (e.g. Fatas and Mihov, 2001), 2) the structural VAR approach (e.g. Blanchard and Perotti, 2002), 3) the sign-restrictions approach (e.g. Mountford and Uhlig, 2005), and 4) the event-study approach (e.g. Ramey and Shapiro, 1998). Typically in this literature government spending and taxes include all levels of government, and are defined net of social transfers. More specifically, government spending is the sum of general government consumption and investment, while net taxes is defined as general government current receipts less current transfer and interest payments.

As is true of nearly all countries, US general government consumption and investment and US general government net taxes are only available at a quarterly frequency. So since the simple baseline VAR model requires data at a monthly frequency, it is necessary to find proxy variables for government consumption and investment and government net taxes just as real GDP (RGDP) and the GDP deflator have been proxied by industrial production and the PCEPI respectively.

In applied macroeconomics, proxy variables typically satisfy two main requirements. First, the proxy variable should measure the equivalent characteristic of a reasonable subset of the variable being proxied. Secondly, the contemporaneous growth rates of the proxy variable and the variable being proxied should be correlated (i.e. have a relatively high Pearson’s r value).

Compensation of employees, received: Wage and salary disbursements: Government (B202RC1), a component of US general government consumption, and Total Public Construction Spending (TLPBLCONS), a component of US general government investment, are both available at a monthly frequency back to January 1993. I shall term the sum of these two variables GWSDTPCS for Government Wage and Salary Disbursements and Total Public Construction Spending. Here is a graph of the natural log of GWSDTPCS and Government Consumption Expenditures & Gross Investment (GCE) since 1993Q1.

GWSDTPCS is a subset of general government consumption and investment, and it ranges from 46.2% to 53.3% of GCE from 1993Q1 through 2015Q1. So it would appear that the first proxy variable requirement is well satisfied.

Now we must check to see if the two variables are correlated. Here are the results of regressing the logged difference (i.e. the growth rate) of GCE on the logged difference of GWSDTPCS and the corresponding scatterplot with the Ordinary Least Squares (OLS) regression line.

The R-squared value is approximately 0.473. Since the growth rates are positively correlated, the Pearson’s r value is +0.688, which is about average for a macroeconomic proxy variable. So it would appear that the second proxy variable requirement is well satisfied. Thus we conclude that GWSDTPCS is a suitable monthly frequency proxy for general government consumption and investment.

Personal Current Taxes is not available at a monthly frequency. However Personal Income (PI)    and Disposable Personal Income (DPI) are available at a monthly frequency, and Personal Current Taxes is simply Personal Income less Disposable Personal Income. Personal Current Taxes, Contributions for government social insurance, domestic (A061RC1), Personal current transfer payments: To government (W062RC1M027SBEA) and Compensation of employees: Supplements to wages and salaries: Employer contributions for government social insurance (B039RC1M027SBEA) are all components of general government current receipts, and are all available at a monthly frequency back to January 1959. Personal current transfer receipts: Government social benefits to persons (A063RC1) is a component of current transfer and interest payments, and is also available at a monthly frequency back to January 1959. I shall term the sum of these monthly current receipts, less the monthly current transfer, Net Personal Taxes, although it includes the employer contribution for government social insurance. This is because all of these series are found in the Bureau of Economic Analysis (BEA) website under the Personal Income category.

General government current receipts less current transfer and interest payments can be calculated by taking Government Current Receipts (GRECPT) and subtracting Government current transfer payments (A084RC1Q027SBEA) and Government current expenditures: Interest payments (A180RC1Q027SBEA). I shall term this series Net Taxes. Here is a graph of the natural log of Net Personal Taxes and Net Taxes since 1959Q1.

Net Personal Taxes is a subset of general government current receipts less current transfer and interest payments, and it ranges from 48.0% to 86.6% of Net Taxes from 1959Q1 through 2015Q1. So it would appear that the first proxy variable requirement is well satisfied.

Now we must check to see if the two variables are correlated. Here are the results of regressing the logged difference (i.e. the growth rate) of Net Taxes on the logged difference of Net Personal Taxes and the corresponding scatterplot with the Ordinary Least Squares (OLS) regression line.

The R-squared value is approximately 0.813. Since the growth rates are positively correlated, the Pearson’s r value is +0.901, which is at the upper limit for a macroeconomic proxy variable. So it would appear that the second proxy variable requirement is extremely well satisfied. Thus we conclude that Net Personal Taxes is a suitable monthly frequency proxy for general government current receipts less current transfer and interest payments.

In Part 2 we’ll check to see if government consumption and investment and if government net taxes are correlated with the output level or the price level in the age of ZIRP.

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

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

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.

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.

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.

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

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.

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.

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.

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

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

In particular we are going enter the next two currencies with the largest relative weights in the Real Trade Weighted U.S. Dollar Index: Broad (TWEXBPA), namely the Mexican peso (11.9%) and the Japanese yen (6.9%). To estimate the real exchange rate (RER) of these currencies in terms of the US dollar I computed the ratio of the Bank for International Settlements (BIS) Real Broad Effective Exchange Rate for each currency area divided by the BIS Real Broad Effective Exchange Rate of the US. I term these ratios RERMXUS and RERJPUS.

Here are the graphs of the natural logs of SBASENS and the real exchange rates.

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

Using the Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests I find that the order of integration is one for all three series. I set up two two-equation VARs in the log levels of the data including an intercept for each equation. Most information criteria suggest a maximum lag length of two for both VARs. The LM test suggests that there is no problem with serial correlation at this lag length in either VAR. The AR roots table suggests that the VARs are dynamically stable.

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

Then I re-estimated the level VARs with one extra lag of each variable in each equation. But rather than declare the lag interval for the two endogenous variables to be from 1 to 3, I left the intervals at 1 to 2 and declared the lag of each variable to be exogenous variables. Here are the Granger causality test results.

Thus, the results are as follows:

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

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

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

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

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

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

With the log of the Mexican monetary base, the Mexican bank funding rate, the effective fed funds rate and the log of the real exchange rate of the Mexican peso in terms of the US dollar added to the baseline VAR model, a majority of the information criteria suggest a maximum lag length of three. An LM test suggests that there is no problem with serial correlation at this lag length. An AR roots table shows the VAR to be dynamically stable at this lag length.

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

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

The Johansen’s Trace Test indicates that there exists five cointegrating equations at this lag length, and the Maximum Eigenvalue Test indicates that there is one. In any case, this is expected, since we already have evidence that the US monetary base is cointegrated with industrial production.

As before, the response standard errors I will show are analytic, since Monte Carlo standard errors change each time an Impulse Response Function (IRF) is generated. Here are the responses to the US monetary base and to real exchanges rates in the seven-variable VARs.

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

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

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

The IRFs also show that a positive 2.0% shock to the US monetary base in month one leads to a peak increase in the real exchange rate of the Japanese yen in terms of the US dollar of 1.1% in month seven. In turn, a positive 2.1% shock to real exchange rate of the Japanese yen in terms of the US dollar in month one leads to a peak increase in the price level of 0.089% in month three.

Why do the Mexican peso and the Japanese yen appreciate with respect to the US dollar in response to a positive shock to the US monetary base?

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

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

An increase in the real exchange rate of foreign currency in terms of the US dollar can make US goods and services more competitive with goods and services priced in that currency, both here and in that currency area, and it can raise the price of goods and services imported from that currency area, which may be reflected by an increase in the US price level.

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

Tune in next time and find out.