3.3.1 Variation in economic activity across states
Figure 3.1 presents evidence on the variation in economic activity across states in the US. States are sorted into five portfolios in each time period conditional on an economic variable of interest. The portfolio average with respect to the conditioning variable are then plotted over time. Panels A-D present the portfolio time series using the conditioning variables real GDP growth per capita, output gap, the demeaned unemployment rate, and inflation rate respectively.2
There is a wide dispersion across states for all the economic variables considered. For example, the difference between portfolio 5 and portfolio 1 for real GDP growth per capita at any given point is in excess of 5% across the full sample. In terms of a relative magnitude for this cross-sectional variation, the time-series average standard deviation of real GDP growth per capita at the aggregated US-level is 2.2%. The cross sectional variation is therefore economically significant.
A closer look at aggregate recessions periods is also revealing. For example, in 2001, 40% of states were in positive real GDP growth territory. This growth is despite the year being a NBER defined recession period. In fact, the top 20% of states had an average economic growth of around 4% that year. It is thus clear that U.S. states can be in quite varying business cycle conditions during aggregate recessions.
One may think that the same states are always placed in the same portfolio due to state fixed effects. However, Panels B and C, which present output gap and unemployment rates demeaned, show that the variation holds even controlling for long-run state averages. For example, following the financial crisis, the 20% of worst effected states saw unemployment rates 5% above their average unemployment rate. At the same time, there was another 20% of states with unemployment rates less than 1% over their long run average.
As well as there being variation in economic activity across states, Panel D shows there is also none-trivial dispersion in prices across states. Inflation rates are computed from state-level price indexes based on micro-price data,3and the variation shows that the prices on the same individual products change significantly across US regions. The average
2The state-level output gap is estimated from the cyclical component of the Hodrick and Prescott (1997) filter on real output. I have also computed output gap with Hamilton (2018) proposed methods.
Results are qualitatively similar, with even more variation using Hamilton (2018).
3see Hazell et al. (2020) for more details.
cross sectional standard deviation (final column of Table 3.1) of the resulting state-level inflation rates is in excess of 1%.
3.3.2 Taylor rule residuals at a state-level
What does this variation mean in a monetary policy context? To explore this question, I calculate the optimal federal funds rate for each state, using a simple Taylor rule
ri,t∗ = 2 +πi,t+ 0.5(πi,t−2) + (u∗t −ui,t) (3.1) whereπi,t is the inflation rate of state iat timet,ui,t is the unemployment rate of statei at timet, and u∗t is the long-run natural rate of unemployment for the US at timet. The rule follows the Bernanke (2015) suggested adjustment to the original Taylor (1993) rule with the coefficient on the unemployment gap set at 1 rather than 0.5.4
Figure 3.2 presents analysis on the variation of the optimal federal funds rate across states. In Panel A, states are sorted into five portfolios at each date conditional on their optimal rate. The portfolio average optimal rates are then plotted over time. I also plot the actual federal fund rate for comparison. Given the dispersion in the economic variables behind the Taylor rule, it is not surprising to see that there is also very large dispersion in the optimal federal fund rates.
Each state’s Taylor rule residual T Ri,t = r∗i,t−rt is the difference between the optimal rate at time t and the actual federal funds rate at time t. Figure 3.2 Panel B presents variation in this variable across states. In the 1990s, when the median optimal fed fund rate almost exactly matches the actual fed fund rate (i.e. the Taylor rule fits very well in the aggregate), the difference between portfolio 1 and portfolio 5 averages at 5%. This shows there were economically meaningful Taylor rule residuals at the local level, even in a period where there was close to no residual at the aggregate level.
Table 3.2 presents more analysis on the Taylor rule residuals over 1989-2009.5 The first row implements the Taylor rule in equation (3.1) at the US aggregate-level as a proof of concept. The first column shows the correlation between the US Aggregate Taylor rule rate and actual fed funds rate is over 90% in this period. In other words, the Taylor rule
4In a similar exerise, Malkin and Nechio (2012) apply the Taylor rule to four U.S. regions: Northeast, Midwest, South, and West. However, they do not study the more granular cross-section of state-level Taylor rule implied rates.
5I have remove the dates post 2009 as the lower bound period restricted the flexibility of the Federal Reserve Board for reduce interest rates.
is a good overall fit and broadly describes the Federal Reserve Board’s monetary policy behaviour.
The remaining rows, which look at various states within the US, show a much worse fit at the state-level. In the best case, South Carolina has a correlation of 75%, while in the worst case Mississippi (“MS”) has a correlation of only 8%. The other columns look at the variation in Taylor rule residuals. The minimum and maximum show that, in the extreme, states can have federal fund rates which are double digits away from what their local economy requires at that time. On top of this, the mean of the absolute Taylor rule residual (final column) shows states are consistently a long distance from their optimal rates. While for the US aggregate the mean distance is less than 1%, individual states are typically over 2% away from their Taylor rule implied optimal rates.
As a case study, Figure 3.3 plots the Taylor rule optimal rate for Florida and North Carolina. These are two states that are relatively close together geographically within the US. Nevertheless, there are large deviations in their optimal policy rate over time. In the 1990s, Florida had high unemployment and thus an optimal policy rate close to zero.
At the same time, North Carolina was enjoying much stronger economic conditions, and had a higher optimal federal funds rate. In fact, at times during the 1990s the federal funds rate was too low from North Carolina’s perspective. Strong economic conditions for states like North Carolina prevented the Federal Reserve Board from cutting rates for the benefit of Florida, and therefore meant that Florida had too low an interest rate. The roles reverse in 2000s, however, with Florida (North Carolina) requiring a higher (lower) federal funds rate given their economic outlook in this decade.
3.3.3 Summary of motivating evidence
This section has documented strikingly large cross sectional variation in economic con-ditions across U.S. states. The variation is economically meaningful in monetary policy context, as demonstrated with Taylor rule residuals. These findings motivate the remain-der of the paper, which explores how this heterogeneity can be used to identify the effects of monetary policy. Specifically, it will use GIV methods, which have been designed to exploit local idiosyncratic shocks in the cross section to make causal identification in the aggregate.