# Recession Probabilities for all 50 States

A couple of weeks ago, I came across an article in The Atlantic titled “What on Earth is Wrong with Connecticut.” The article is about the condition of Connecticut’s economy and state budget, and inspired me to consider two questions that I had been thinking about for some time – (1) are any U.S. states currently in recession, and (2) has there been any historical pattern around national recessions regarding which states enter recession earlier than others?

DATA & METHODOLOGY

In order to try and answer these questions, I used data on the month-over-month (MoM) percentage change in total payroll employment in all 50 states (and Washington DC) from 1990 through May, 2017. While recessions are typically defined as a decline in output, not employment, national employment recessions and output recessions have historically been highly correlated. Additionally, the data for state employment goes back further then the data for state GDP, at least on FRED, and the the employment data is measured at a higher frequency. To give a sense of what the raw data looks like, below is the MoM percentage change in total payroll employment for Minnesota:

To estimate recession probabilities for each state, I use a version of the Markov Switching (MS) model developed in Hamilton (1989). In this model, there are two regimes, or “states of the world”. When Hamilton estimated this model using data on U.S. GNP, it returned two clear regimes – “expansion” and “recession”. Furthermore, as a byproduct of estimation, the model provided estimated probabilities for each regime at each date in the history of the data, and these probabilities matched up very closely with the official recession dates in the U.S.

I decided to estimate an MS model independently for each U.S. state, using the MoM percentage change in total payroll employment as the data. Similar estimation strategies have been undertaken before, for example, see Owyang, Piger, and Wall (2005) (pdf).  After censoring the data to ignore large outliers that greatly influenced estimation in approximately 10 states (such as the massive decline in employment in Louisiana following Hurricane Katrina), I fit the following Markov Switching model to each U.S. state, independently:
$y_t = \mu_0 + \mu_1 s_t + \rho(y_{t-1}-\mu_0-\mu_1 s_{t-1}) + \varepsilon_t$
$\varepsilon_t \sim N(0,\sigma)$
And $s_t \in \{0,1\}$ evolves according to an exogenous first order Markov process, with transition matrix given by:
$P= \begin{bmatrix} p_{00} & p_{01} \\ p_{10} & p_{11} \end{bmatrix}$

I performed Bayesian estimation, with the following priors on the regression coefficients:

• Annual expansion growth rate $\sim N(2.4,0.85)$
• Annual recession growth rate $\sim N(-2.4,0.85)$
• AR(1) term $\sim N(0.25,0.06)$

Note that I am using the annual growth rate here instead of the monthly growth rate, since it is a more intuitive number. These priors imply 99% prior confidence intervals for the unconditional annual growth in expansions and recessions of roughly $[0\%,4.8\%]$ and $[-4.8\%,0\%]$, and a 99% prior confidence interval for the AR(1) of roughly $[-0.4,0.9]$.

For the transition probabilities, the prior probability of staying in expansion next month if the state was in expansion this month is set to 0.9, and the prior probability of staying in recession next month if the state was in recession this month is set to 0.8, each with 5 prior observations.

RESULTS

In regard to the first question – are any states currently in recession, the answer is probably no. As of May, 2017, only Idaho had a recession probability greater than or equal to 50% (and it was exactly 50%). However, May was the first month in which the recession probability exceeded 49%, and based on earlier research on national recessions, a recession probability typically has to exceed 49% for at least two months in a row to reliably signify the onset of a recession.

 State Rec. Prob ID 50% NJ 40% NH 39% OK 34% KS 32%

As far as Connecticut is concerned, it currently has a recession probability of 0%, but it is estimated to have the slowest expansion growth rate among all 50 states, which could be a result of the factors discussed in the article, or simply due to out-migration (and disentangling these two causal factors is not something I am able to do).

 State Exp. Growth Rate NV 3.9% UT 3.6% … … PA 0.9% CT 0.8%

In regard to the second question – has there been any historical pattern regarding which states enter recessions “first” before the beginning of a national recession, I don’t find any sort of pattern. The two images below show monthly employment recession probabilities for all 50 states (plus DC) over time, starting in 1990 (click twice to enlarge).

CONCLUSION

I used an MS model with AR(1) dynamics to estimate historical recession probabilities in all 50 U.S. states. For the most recent month for which data is available, May 2017, I found that there were probably no U.S. states in recession, although if payroll employment growth is again negative in Idaho in June, it would likely indicate an employment recession in Idaho. I also found that there does not seem to be a consistent pattern regarding which states enter recessions first, prior to a national recession. In other words, there are no states that have served as reliable “leading indicators” for the national economy over the last three business cycles. Finally, while Connecticut is the wealthiest state in the U.S. in per-capita terms, it has had the slowest rate of increase in employment during expansions over the past 25 years. The current methodology does not allow me to determine any factors that may be causing this slow growth.

As new data is released, I will keep updated graphs and estimates here: http://adamjcheck.com/state_rec.html

# A Liquidity Trap in an AS/AD Framework (Part I)

First post in a while. This part just sets the basic AS/AD model up. Part II will introduce the zero lower bound (ZLB), which is the fact that interest rates can’t fall below zero, and show that allowing for the ZLB leads to some interesting & surprising changes to the basic model. Part III will show how an economy can become trapped in a deflationary spiral (with inflation and output both falling forever) when the Fed hits the ZLB. Part IV will recommend policies to help avoiding the ZLB.

Before we talk about the ZLB, let’s discuss the basic math of the AS/AD model as presented in the intermediate textbook by Jones (2014). We will eventually end up with three (and then two) equations, which I discuss below in more detail. These three equations are:

IS: $\tilde{Y}_t = \bar{a} - \bar{b}(R_t-\bar{r})$
MP: $R_t = \bar{r} + \bar{m}(\pi_t - \bar{\pi})$
AS: $\pi_t = \pi_{t-1} + \bar{v} \tilde{Y}_t + \bar{o}$

The IS Curve describes how output, $\tilde{Y}_t$, changes in response to a change in the real interest rate, $R_t$. It is given by: $\tilde{Y}_t = \bar{a} - \bar{b}(R_t-\bar{r})$. Here, $\bar{a}$ is a demand shock, $\bar{r}$ is the marginal product of capital (you can think of this as the return that a businesses in the economy will receive if they buy one more machine). A good way to think about the real interest rate, $R_t$, is the return that businesses would receive if they put their money in a savings account. Therefore if the real interest rate increases, then businesses will be more likely to put their money in a savings account rather buying a new machine, and investment will decline.

The second equation is the monetary policy (MP) curve, which describes how the central bank changes the real interest rate in response to changing inflation: $R_t = \bar{r} + \bar{m}(\pi_t - \bar{\pi})$. Here, $\pi_t$ is the actual inflation rate this year, and $\bar{\pi}$ is the central bank’s inflation target. This rule says that as inflation increases, the central bank will raise interest rates (with the intention of decreasing investment, and therefore cooling the economy off).

The third equation is the aggregate supply (AS) curve. This equation describes how firms change prices, and therefore it describes how inflation changes over time. It is given by: $\pi_t = \pi_{t-1} + \bar{v} \tilde{Y}_t + \bar{o}$. Here, $\bar{o}$ is an inflation shock, and $\pi_{t-1}$ is the inflation rate last year. This equation says that if short-run output, $\tilde{Y}_t$, increases, then businesses are faced with a lot of extra demand, so they will raise prices. The story that we tell is that if businesses have a lot of demand, then they can raise prices by more than usual without fear of losing customers. If businesses are raising prices, then there is more inflation.

Taken together, we have:
IS: $\tilde{Y}_t = \bar{a} - \bar{b}(R_t-\bar{r})$
MP: $R_t = \bar{r} + \bar{m}(\pi_t - \bar{\pi})$
AS: $\pi_t = \pi_{t-1} + \bar{v} \tilde{Y}_t + \bar{o}$

We can combine the IS & MP curves to get the aggregate demand curve. Now we have our two equations:
AD: $\tilde{Y}_t = \bar{a} - \bar{b} \bar{m}(\pi_t - \bar{\pi})$
AS: $\pi_t = \pi_{t-1} + \bar{v} \tilde{Y}_t + \bar{o}$

Aggregate demand (AD) combines two relationships. First, if inflation rises, the central bank will increase interest rates. Second, if interest rates rise, investment will fall, leading to a decrease in output. Therefore, as we can see in the AD curve, if inflation increases, output will fall. Note that this is not just a law of nature – the reason that output falls when inflation rises is due to the policy of the central bank. This will be very important in future posts.

Graphically:

This summarizes the model as presented in Jones (2014). However, this analysis completely neglects the zero-lower bound, i.e. the fact that nominal interest rates on savings accounts can’t go below zero (if interest rates were negative, then people would just keep their money at home rather than put it in the bank). Therefore, if the MP curve calls for the central bank to set a very negative real interest rate, the central bank will not be able to do it – this problem is called a liquidity trap, and it’s where policymakers around the world have found themselves stuck ever since 2009.

Because the model, as currently derived, does not take this possibility into account, it features a misspecified monetary policy curve (and therefore a misspecified AD curve, since MP is used to derive AD). How to fix the MP curve to allow for the fact that nominal interest rates can’t go negative is the subject of my next post.

# Stochastic Volatility Approximations

This post is more geared to economists/econometricians, and will compare two different approximations that are frequently used when estimating stochastic volatility.

Basically, stochastic volatility means that the variance of a process can change over time. This is a commonly observed phenomenon in economic data.  For example, if we look at the quarterly growth rate of GDP since 1948, we can see that GDP bounced around a lot before 1980, but then it settled down until the financial crisis hit in 2008.

It’s a little confusing at first, but the main problem is that the time-varying volatility has a Chi squared distribution, so that you can not use the Kalman Filter to estimate the time-varying volatility directly.  You can use a particle filter, but the most common way to undertake the estimation is to use a 7-point mixture of normals approximation that was introduced Kim, Shephard, and Chib (1998, ReStud).  However, a better 10-point approximation to the distribution was introduced in Omori, Chib, Shephard and Nakajima (2007, Journal of Econometrics).

Since a large body of research has used the earlier, 7-point distribution, I wanted to see how much better the 10-point distribution performed in practice.  To do the comparison, I generated 100 fake time series, each of length 100 periods, and all with stochastic volatility.  In the standard set-up, the volatility follows a random walk:

h_{t} = h_{t-1} + e_{t}
e_{t} ~ N(0,sig2)

Since the variance of this random walk, sig2, controls how much the volatility can change over time, I repeated the exercise for four different values: 0.01, 0.05, 0.10, and 0.15.  To compare the approximations, I performed Bayesian estimation using the Gibbs sampler, with 1,000 burn in draws and 9,000 posterior draws. Since I generated the data, I knew the true underlying values of both sig2 and the entire time path of volatilities, h_{t} for t = 1:100. Therefore, I could compare the estimates I got using each of the approximations to the true values.

To judge the approximations I used four criteria: the bias of the average estimated volatility path, the mean squared error (MSE) of the average estimated volatility path, the bias of the sig2 estimate, and the MSE of the sig2 estimate. The results are as follows, with the bolded numbers representing the better performance.

The results are actually fairly mixed, although it does appear that the mixture of 10 normals performs very slightly better. The differences are not economically meaningful, however.

So what have we learned?  It probably isn’t worth re-estimating previous work that had used the 7-point mixture, since the gains from using the 10-point are so small.  But, for a young economist, it wouldn’t hurt to use the 10-point (it is more accurate, no more difficult to code, and only negligibly increases the run-time of the estimation procedure).

Via Timothy Taylor, the Bank of International Settlements (BIS) has a new report out on deflationary episodes.  Looking at the five years prior to an episode of deflation and at the five years after inflation, they do a kind of diff-in-diff estimator of whether the deflationary episode resulted in slower growth.  They find that, with the exception of asset price deflations, deflation alone does not lead to lower growth.

This is not that surprising to me.  When I first learned about deflationary spirals, I found the idea captivating, and it made a lot of intuitive sense.  However, upon reflecting on my own behavior, I realized that I do not behave the way the standard story goes.  For example, technology goods have famously gotten cheaper through the years, but I still line up to buy the latest edition, even though I know the same product will be cheaper in a year.

And it’s not just me.  Personal consumption expenditures on video, audio, photographic, and information processing equipment and media has not only steadily grown through the years, it has actually doubled as a percentage of total PCE since the 1960’s (from 1% to 2%).

In an industry where there is consistent deflation, there has been massive growth.  This certainly seems consistent with the story told by the BIS.

# Why Hasn’t There Been More Disinflation?

The Phillips curve, a relationship between the unemployment rate and inflation, has come under sharp criticism lately.  Contrary to what the Phillips curve would predict, the massive uptick in unemployment during the Great Recession has not resulted in much deflation.  Instead, inflation has mostly bounced between 1 and 2 percent over the past several years.

A possible contributing cause has been household expectations of inflation.  Although inflation since the beginning of the Great Recession has averaged around 1.5 percent per year, households have consistently predicted inflation to be 3 percent.  If the Phillips curve is augmented to include these expectations, then it explains that data very well.

But that just pushes the question one step further –  Why have people been consistently overestimating the inflation rate?  As we can see in the graph below, this positive bias is a relatively recent phenomenon, as the difference between the forecast and actual inflation tends to bounce around zero for the majority of the period 1978-2014.   Only recently (and for a couple of years in the mid-1990s) has inflation forecast been consistently upwardly biased.

A forthcoming paper by Coibon and Gorodnichenko explains this bias by showing that household inflation expectations have tracked oil prices quite closely.  They hypothesize that this is due to the undue influence gasoline prices play in the minds of consumers (it is the one price that virtually everyone that drives sees multiple times per day, and nightly news reports obsess over oil prices).

In contrast, Robert Waldmann has a post up today on Angry Bear which asserts that the reason for the higher inflation expectations has been due to the right-wing paranoia over high inflation.  He thinks that constant cries on Fox News that inflation has been too high (or will soon explode)  has led to the upwardly biased inflation expectations.