**A Mark Sadowski post**

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

**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.**

*not*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.