## 28 May 2016

### Secular Stagnation

Proponents of secular stagnation love to show the following graph
as evidence that the US labor market has hardly recovered from the last recession, making the last eight years a so-called 'jobless recovery.' Explanations for this vary, but two seem to be most popular:
1. There is a savings glut in the United States, meaning that the nominal interest rate that is required for savings/investment equilibrium is significantly negative, resulting in a persistent aggregate demand shortfall.
2. Recessions have negative effects on potential output/employment, making complete recover to full employment unlikely without significant government intervention.
The narrative seems to make sense: to the extent that the employment to population ratio is indicative of the state of the American labor market, the recovery has, to a large extent, been 'jobless,' and real GDP remains far below it's 1990 to 2007 trend:
Furthermore, the real federal funds rate remains below normal levels, a prediction in conjunction with number 1 above:
I'm not entirely convinced of this case, though. For one thing, the employment to population ratio is hardly a good indicator of the labor market -- employment simply should not revert to the same proportion of the population irrespective of demographic concerns. Part of the reason economic growth was relatively rapid in the 1980's is that there was a secular increase in the employment to population ratio driven by women entering the labor force. Similarly, part of the reason post-2007 growth has been relatively slow is because of a secular decline in the employment to population ratio driven by an aging population:
Since the NBER recession trough in June 2009, the employment to working age population ratio has recovered a lot more than the employment to population ratio, and this is with data that only goes until March of 2015. Also, broader measures of unemployment that include those 'marginally attached' to the labor force -- people who have expressed a desire for work in the last 12 months -- as well as people who are currently part time but would like to be full time show a much more robust recovery in employment than the employment to population ratio suggests.
The idea that employment remains significantly depressed in the United States is dubious. Yes, there has been a significant decline in employment levels that has not recovered, but this decline is most likely secular and, while there is still room for improvement in the labor market, it is clear that the employment to population ratio vastly exaggerates how much room there actually is.

What about real GDP? Hasn't the decline there been significant and persistent? Yes, but most of that can be explained by the largely demographically driven slow growth of employment since 2008, leaving the rest to be explained by low productivity growth. Does it makes sense to suggest that recessions caused by drops in aggregate demand have negative effects on productivity?

Unfortunately the theory in this area is rather lacking; while there are endogenous growth models, their real ability to explain TFP growth remains extremely dubious in my opinion -- when the causal link between, e.g., R&D employment and TFP is just assumed, I don't see there being much of a possibility for success. That being said, it certainly seems reasonable that long spells of detachment from employment result in the eroding of skills, for example, so the argument remains undecided in my opinion.

But I digress, the most important part of secular stagnation is the notion that the labor market has significantly more slack than it actually does, and thus it seems that the likelihood of a persistent decline in employment is small.

## 27 May 2016

### Sumner on Philosophy

"If my philosophy is wrong then my market monetarism is equally wrong."

Yes.

## 21 May 2016

### Estimating the Output Gap for the US and the Euro Area

Following after this post from Menzie Chinn, I decided to try to estimate the output gap for the US and the Euro Area.

This method has two basic steps. First you assume that the Phillips curve takes the form
$$\pi_t = \bar\pi + a (y_t - \bar y_t) + \epsilon_t$$
where $\pi_t$ is the current inflation rate, $\bar\pi$ is the inflation target and/or the average inflation rate over the sample period, $y_t$ is the natural log of real GDP, $\bar y_t$ is potential GDP, and $\epsilon_t$ is a random shock.

Using an HP filter to determine 'potential' GDP, you then run a regression to determine the slope of the Phillips curve, which allows you solve for potential GDP:
$$\bar y_t = y_t + \frac{\bar\pi-\pi_t}{a} + \frac{\epsilon_t}{a}$$
Since the shock term is still present, it is necessary to smooth the data again. I used an HP filter for both this as the previous smoothing (discerning potential GDP), but you can also use a lowess/LOESS filter, if you prefer, the results are not different enough to be worthwhile, although sometimes the lowess result seems more plausible when eyeballing.

I digress, this new filtered series should provide a plausible estimate of potential GDP somewhat like this:

One important note is that I used core CPI for the US and the GDP deflator for the EA. Using the GDP deflator for each works well, but core CPI provides an estimate closer to the CBO output gap for the US, so I stuck with it there. Also core CPI implies an implausibly small slope for the Phillips curve in the Euro Area, which results in large swings in potential GDP and implies a large and increasing output gap since 2008.

I also tried this same process for Japan and the UK, but both of them gave highly implausible estimates of potential GDP -- the slope of the Phillips curve for the UK was implausibly small (even using the GDP deflator), resulting in a path for potential output similar to that of the Euro Area using core CPI. Japan's Phillips curve appears of have a negative slope, making the recent small increase in inflation imply a hugely negative output gap ($\approx -40$%).

Also, here is a comparison of my estimate of the US output gap and that of the CBO, as well as a comparison of the same data using an HP filter and a lowess filter:

Note that this data starts Q1-1997 and ends Q1-2016, just like the previous data (the lowess filter in python has the unfortunate side effect of making the x-axis labels really annoying to deal with). If you would like to play around with the IPython notebook, here it is.

## 14 May 2016

### Non-Walrasian Macro

The typical framework used by economists to make models renders generating monetary non-neutrality nigh impossible without the use of dubious assumptions like price adjustment costs or the existence of a 'Calvo fairy' that chooses at random when a firm can or cannot change its price.

Otherwise, it is posited, the firm would just set its price to whatever level is consistent with full employment at all times, rendering monetary policy useless at doing more than simply changing the inflation rate. Brushing aside possible empirical issues with this contention, this poses significant political problems for many economists; if monetary policy is impotent at all times, then either the economy is always at 'potential' thus rendering all intervention unnecessary, or the only viable means of economic stabilization is fiscal. As both of these options are highly undesirable to everyone who doesn't work at the St. Louis Federal Reserve of the University of Chicago, the problem must be solved.

This is when most of the profession turned to finding microfoundations for price stickiness (only to find that none of them are consistent with the actual behavior of individual prices, but never mind that) and thus New Keynesian economics was born. We now have the expectations augmented Phillips curve, in all its reduced form glory derived from a set of specific if highly unrealistic assumptions about the world. There is one point of interest here, however: if you remove both rational expectations and the dynamic aspect of the model, the basic three equation New Keynesian model reduces to IS-LM with sticky instead of completely stuck prices -- think Krugman's 1998 paper.

Evidently we spent 20 years trying to develop a model that has the exact same insight into the economy as we were able to get from a much simpler model from 1936 (Occam's razor, anyone), but at least this one can pretend to be quantitative (Smets-Wouters). Now I will not pretend to minimize the advantages of utility maximization when it comes to analyzing situations; sometimes it really helps to use utility maximization when you cannot simply draw an upward and downward sloping curve and call it a day (hooray for OLG models!), but when it comes to qualitative models of the business cycle, nothing beats IS-LM (say what you will about the consumption function, just have Y = a*G, for all I care).

Maybe it's time we took this all in a different direction, though. The main reason we went on the rabbit trail of New Keynesianism to get back to IS-LM was because of Walrasian ideas about supply and demand. That is, by some force of magic the market will determine the equilibrium price instantly (hence the rule that quantity supplied equals quantity demanded). But does this really make sense? even assuming individual firms knew the exact shape of their demand curve, is it reasonable to assume that they would be able to determine what (nominal) price to set so that their relative price is at the profit maximizing level? Or, more succinctly, how do firms magically know what price to set if there is no real Walrasian auctioneer?

But if we don't ignore tatonnement -- that gradual approach of a price to its equilibrium level -- then we naturally get Phillips curves everywhere, as firms slowly increase prices to fend of excess demand and lower wages to head off excess supply (of course wage bargaining is two sided but bear with me). In fact, replacing $D=S$ in models with $\dot{p} = \alpha(D-S)$ could circumvent the entire need for New Keynesian models; let the nominal rigidities run wild as freshwater economists cower in fear of non-Walrasian macro.

Not only would this alleviate the need for New Keynesian models, it would replace them with much simpler that are what I would like to call 'semi-microfounded.' That is models would have the typical upward and downward sloping curves -- who needs calculus -- and then have a specification for how tatonnement occurs. For instance, a labor market would have a labor demand equation: $L_d = -a W$ and a labor supply equation $L_s = b W$. Then tatonnement would be $\dot{W} = \alpha(L_d - L_s)$. Did the equilibrium wage move? Oh no, I guess we'll have to find it since uncle Walras can't just tell us what it is any more.

## 07 May 2016

### Austerity

Upon realizing that I could easily get the Cyclically Adjusted Primary Balance data from the IMF as well as Real GDP data from the OECD without expending an extreme amount of energy, I decided to add to the empirical findings that already exist about austerity. I also sought to answer some of the concerns that Scott Sumner likes to express about every attempt at drawing a correlation not provided by Mark Sadowski.

I composed one list that included the Euro Area and one that did not (only to make Sumner shut up) and ran a regression taking the change in the CAPB between 2009 and 2014 as the x variable and the growth of real GDP between 2009 and 2014 as the y variable. The first list included Austria, Belgium, Canada, the Czech Republic, Germany, Denmark, Spain, Finland, France, Greece, Ireland, Italy, Japan, the Netherlands, Portugal, the United States, and the United Kingdom while the second list only had the Czech Republic, Japan, the United States, and the United Kingdom. Note that all of the countries were either at the zero lower bound or otherwise in a liquidity trap (defined as a case in which lowering the nominal interest rate to zero could not have resulted in full employment).

The second list was too small to yield any useful data, but the first list suggested that the coefficient on the change in the CAPB is about $-1.27$, with a p value of $9.2274 \cdot 10^{-4}$ (t-stat is $-4.112416418$). The second list did have a negative coefficient of about $-0.35$, but 5 samples is really way too few to actually conclude anything (maybe this is one of the reasons Sumner wants to remove the Euro Area).
One interesting fact that I noticed, that anyone could check in about 5 minutes if they cared to download the publicly available spreadsheet of CAPB from the IMF, is that, at least between 2009 and 2014, contrary to what Sumner claims, the US did less austerity than Europe. How much less? This much: $-0.3359236583554$. That is, the CAPB increased by about a third of a percentage point less in the US than in the Euro Area. If you included the UK, it would be even worse.

Why don't I include countries like Iceland in my calculations? Simple: they did not go to the zero lower bound in 2009 and they were never close to the zero lower bound, thereby making their addition to a regression about the effect of austerity in a liquidity trap a complete waste of time.

I'm still not perfectly happy with this assessment because I wanted to use the real GDP to working age population ratio instead of simply real GDP, as it would have made the intercept for the regression a little bit less uncertain -- while steady state real GDP growth is indeed quite variable, adjusting for demographics seems to solve the problem most of the time. Unfortunately FRED has annoying limitations with graphs and data lists, so this is the best I could do without spending more than a day on this.

The main point here is that, excluding countries obviously not at the zero lower bound, austerity is highly negatively correlated with real GDP growth and this correlation persists, even if it is not significant, when you exclude the Euro Area.