fedfunds.R

##
## John Taylor proposed the following rule designed to guide monetary policy:
## i = r* + pi + 0.5 ( pi - pi*) + 0.5 ( y - y*)
## where i is the nominal federal funds rate, r* is the "natural" real federal funds rate (often taken to be 2%), pi is the rate of inflation, pi* is the target inflation rate (for example, 2%), y is the logarithm of real output, and y* is the logarithm of potential output.
## The two basic ideas here are to raise the federal funds rate to one-half the extent that inflation exceeds its target and to lower the federal funds rate to one-half of the percentage that real output falls below its potential.  Implicit in this formulation is that a reasonable rule of thumb applied consistently over time is more likely to achieve a good outcome than is aggressive manipulation of monetary policy.  It is widely believed that central banks have paid close attention to variations on this Taylor Rule in recent years.
## From: http://www.econmodel.com/classic/terms/taylor_rule.htm

calculateTaylorRule = function(natural_ff_rate=2, inflation_target=2)
{
  if ( exists("CPILFESL") == FALSE ) { getSymbols("CPILFESL", src="FRED") }
	if ( exists("GDPC96") == FALSE ) { getSymbols("GDPC96", src="FRED") }
	if ( exists("GDPPOT") == FALSE ) { getSymbols("GDPPOT", src="FRED") }
	
	rstar = natural_ff_rate
	pi = Delt(CPILFESL, k=12)*100
	pistar = inflation_target
	y = log(GDPC96)
	ystar = log(GDPPOT)
	
	i = rstar + pi + 0.5 * (pi - pistar) + 0.5 * ((y - ystar)*100)
	return( i )
}


## 
## Federal funds rate = 8.5 + 1.4 (Core inflation - Unemployment).

## Here "core inflation" is the CPI inflation rate over the previous 12 months excluding food and energy, and "unemployment" is the seasonally-adjusted unemployment rate. The parameters in this formula were chosen to offer the best fit for data from the 1990s.

## From: http://gregmankiw.blogspot.com/2006/06/what-would-alan-do.html

calculateMankiwRule = function()
{
	if ( exists("CPILFESL") == FALSE ) { getSymbols("CPILFESL", src="FRED") }
	if ( exists("UNRATE") == FALSE ) { getSymbols("UNRATE", src="FRED") }
	
	i = 8.5 + 1.4 * (Delt(CPILFESL, k=12)*100 - UNRATE)
	return( i )
}


calculateHybridFF = function()
{
	if ( exists("PCEPILFE") == FALSE ) { getSymbols("PCEPILFE", src="FRED") }
	if ( exists("U6RATE") == FALSE ) { getSymbols("U6RATE", src="FRED") }
	if ( exists("GDPC96") == FALSE ) { getSymbols("GDPC96", src="FRED") }
	if ( exists("GDPPOT") == FALSE ) { getSymbols("GDPPOT", src="FRED") }
	if ( exists("TCU") == FALSE ) { getSymbols("TCU", src="FRED") }
	if ( exists("FF") == FALSE ) { getSymbols("FF", src="FRED") }
	
	a = na.trim(na.locf(merge(FF, Delt(PCEPILFE, k=12), U6RATE, GDPPOT/GDPC96, TCU)))
	a = a[endpoints(a, on="months")]
	names(a) = c("FF", "CPI", "U6RATE", "OUTPUTGAP", "TCU")
	m = lm(a$FF ~ a$CPI + a$U6RATE + a$OUTPUTGAP + a$TCU + 0)
	a$model = predict(m)
	print(cor(a)[,1])
	return( a$model )		
}

plotRules = function()
{
  if ( exists("DFF") == FALSE ) { getSymbols("DFF", src="FRED") }
	if ( exists("USRECD") == FALSE ) { getSymbols("USRECD", src="FRED") }

	a = na.locf( merge(DFF, calculateMankiwRule(), calculateTaylorRule(), Delt(CPILFESL, k=12)*100, UNRATE, USRECD) )
	names(a) = c("DFF", "Mankiw", "Taylor", "CPI", "UNRATE", "USRECD")
	b = na.omit( a[ endpoints(a) ] )
#	b = b["2006::"]
	layout(1:2)

	par(xaxt="n", yaxt="n")
	barplot(b$USRECD, border="grey", col="grey")
 	par(new=T, xaxt="s", yaxt="s")

	plot(b$DFF, main="", ylim=c(min(b), max(b)), ylab="%")
	lines(b$Mankiw, col="red")
	lines(b$Taylor, col="blue")
	lines(b$CPI, col="green")
	legend("topleft", c("Fed Funds", "Mankiw", "Taylor", "Core CPI"), col=c("black", "red", "blue", "green"), lty=c(1, 1, 1), cex=0.5)
	title(main="Fed Funds vs Taylor & Mankiw Rules")
	diff_taylor = b$DFF - b$Taylor
	diff_mankiw = b$DFF - b$Mankiw
	plot_ylim=c(
		min(na.omit(merge(diff_taylor, diff_mankiw, b$CPI))), 
		max(na.omit(merge(diff_taylor, diff_mankiw, b$CPI))))
	par(xaxt="n", yaxt="n")
	barplot(b$USRECD, border="grey", col="grey")
 	par(new=T, xaxt="s", yaxt="s")
	plot(diff_taylor, main="Model Differences & Inflation+Unemployment", ylim=plot_ylim, ylab="%")
	lines(diff_mankiw, col="blue")
	lines(b$CPI, col="green")
	abline(h=0, lty=2)
	par(new=T, xaxt="n", yaxt="n")
	plot.zoo(b$UNRATE, col="red")
	par(xaxt="s", yaxt="s")
	axis(4)
	legend("topleft", c("Fed Funds - Taylor", "Fed Funds - Mankiw", "Inflation", "Unemployment (RHS)"),
		col=c("black", "blue", "green", "red"), lty=1, cex=0.5)
}