**A Mark Sadowski post**

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.