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How Many Equations Should There be in Macroeconomic Models ?

Recently a very old debate among macroeconomists has been reopened (this happens from time to time). Paul Romer decided to discuss a key conference held in 1978 (yes really). Some (including me) think that’s about when the profession took a wrong turn largely following Robert Lucas. But in the discussion until about yesterday, it was agreed that macroeconomics was in a bad way in 1978 and needed to change. Romer particularly criticized a paper presented by Ray Fair at the conference.

This has provoked Ray Fair* to start blogging. I think it is quite important to read his post (so does Mark Thoma). Fair is very unusual, because he works at a University (some small place called Yale) yet he stuck with the approach started by Jan Tinbergen and especially by Jacob Marschak and collegues at the Cowles Commission (then at U Chicago) which was criticized by Lucas. I will follow Fair by calling it the CC (for Cowles Commission) approach. Notably, the approach was never abandoned by working macroeconomists, including those at the Fed and those who sell forecasts to clients who care about forecast accuracy not microfoundations.

Insert: This post is long. The punchline is that I think that a promising approach would be to combine CC models with a pseudo prior that a good model is not too far from a standard DSGE model. This is the sort of thing done with high dimensional VARs using the so called Minnesota prior.
end insert.

There are (at least) two key differences between the CC approach and models developed later. First the old CC models did not assume rational expectations. This has been the focus of the discussion especially as viewed by outsiders. But another difference is that the old models including many more variables and, therefore, many more equations, than the newer ones. The model presented in 1978 had 97 equations. This post is about the second diference — I don’t believe it makes sense to assume rational expectations, but I won’t discuss that issue at all.

With his usual extreme courtesy, Simon Wren Lewis noted advantages of the old approach and, as always, argues both old and newer approaches are valuable and should be explored in parallel.

I have to admit that I don’t intend to ever work with a model with 97 separate equations (meaning 97 dependent variables). But I think that one fatal defect of current academic macroeconomics is that it has been decided to keep the number of equations down to roughly 7 (New Keynesian) or fewer (RBC).

I will start by discussing the costs of such parsimony.

1) One feature of pre 2008 DSGE models which, it is agreed just won’t do is that they assumed there was only one interest rate. In fact there are thousands. The difference between the return on Treasury bills and junk corporate bonds was one of the details which was ignored. The professions response to 2008 has been to focus on risk premia and how they change (without necessarily insisting on an explanation which has anything to do with firm level micro data). Here I think it is agreed that the pre 2008 approach was a very bad mistake.

2) As far as I know (and I don’t know as much as I should) a second omission has received much less attention. Standard DSGE models still contain no housing sector. So the profession is attempting to understand the great recession while ignoring housing completely. Here, in particular, the old view that monetary policy affects output principally through residential investment isn’t so much rejected as ignored (and quite possibly forgotten).

3) Similarly there are no inventories in models which aim to match patterns in quarterly data. I teach using “Advanced Macroeconomics” by Romer (David not Paul or Christine). He notes that a major component of the variance in detrended (or HP filtered) output is variance in detrended inventory investment, then writes no more on the topic. He is about as far from Lucas as an academic macro-economist (other than Fair) can be. Assuming no inventories when trying to model the business cycle is crazy.

4) In standard models, there is one sector. There is no discussion of the distinction between goods and services (except now financial service) or between capital goods and consumption goods. In particular it is assumed that there are no systematic wage differentials such that a given worker would be pleased to move from the fast food sector to the automobile manufacturing sector. Again the micro-econometric research is completely ignored.

5) A lot of standard academic DSGE models assume a closed economy.

6) No one thinks that the wage and price setting mechanisms assumed in either RBC or NK models are realistic. They are defended as convenient short cuts.

7) It is assumed that there are no hiring or firing costs (or unions which object to layoffs). Similarly the assumptions about costs of adjusting capital are not ones that anyone considered until it was necessary to make them to reconcile the data with the assumption that managers act only to maximize shareholder value.

8) Oh yes it is assumed that there are no principal agent problems in firms.

9) It is assumed that markets are complete even though they obviously aren’t and general equilibrium theorists know the assumption is absolutely key to standard results.

10) It is assumed that there is a representative agent even though there obviously isn’t and general equilibrium theorists know the assumption makes a huge gigantic difference.

This means that most of the topics which were the focus of old business cycle reasearch are ignored as are most post 1973 developments in microeconomics.

Before going on, I have to note that when each of these assumptions is criticized, special purpose models which relax the extreme assumptions are mentioned (sometimes they are developed after the criticism). But policy is discussed using the standard models. The assumptions are immune to evidence, because no one claims they are true yet their implications are taken very seriously.

What benefit could possibly be worth such choices ? That is what is wrong with a macroeconomic model with too many equations ? One problem is that complicated models are hard to understand and don’t clarify thought. This was once a strong argument, but it is not possible to intuitively grasp current DSGE models.

One reason to fear many equations is the experience of working with atheoretic vector autoregression (VAR) models which were developed in parallel with DSGE. in VARs the number of parameters to be estimated is proportional to the square of the number of equations. The number of observations of dependent variables is equal to the number of equations. More equations can imply more parameters than data points. Even short of that, large VAR models are over parametrized and fit excellently and forecast terribly. 7 equations are clearly too many. a 97 equation VAR just couldn’t be estimated. The CC approach relied on imposing many restrictions on the data based on common sense. A 97 equation DSGE model is, in pricipal, possible, but ideas about simplifying assumptions which should be made are, I think, based in large part on the assumptions which must be made to estimate a VAR.

If there are many dependent variables but each is explained by an ordinary number of independent variables each of which is instrumented by a credible instrument, then there shouldn’t be a problem with over-fitting. The fact that somewhere else in the model othere equations are estimated does not cause a spuriously good fit for an equation which doesn’t include too many parameters itself.

However, there is another cost of estimating a lot of parameters. The parameter estimation error makes forecasts worse at the same time it makes the in sample fit better. In the simplest cases, these two problems cause identical gaps between the in sample fit and the out of sample forecast. The second problem is absolutely not eliminated by making sure each equation is well identified.

But there is a standard approach to dealing with it. Instead of imposing a restriction that some parameter is zero, one can use a weighted average of the estimate parameter and zero. This is a Stein type pseudo Bayesian estimator.

I will give two examples. In the now standard approach, it is assumed that residential ivnestment is always exactly proportional to non residential investment. In the old approach residential and non residential investment were considered separately. In the pseudo Bayesian approach, one can estimate an equation for the growth of log total investment, estimate equation for the growth of log residential minus the growth of log total investment, then multiply the coefficients of the second equation by a constant less than one.

In another example one can assume that inventory investment is zero (as is standard DSGE models) or estimate net inventory investment as a function of other variables. Adding half the fitted net inventory investment to the standard DSGE model might give better forecasts than either the now fashionable or the old fashioned model.

This is the standard approach used with high dimensional VARs. I see no reason why it couldn’t be applied to CC models.

I see Wren Lewis has a new post which I must read before typing more (I have read it and type the same old same old so you probably don’t want to click “read more”).

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Real Household Net Worth: Look Out Below?

In my last post I pointed out that over the last half century, every time the year-over-year change in Real Household Net Worth went negative (real household wealth decreased), a recession had either started, or was about to.  (One bare exception: a tiny decline in Q4 2011, which looks rather like turbulence following The Big Whatever.) Throughout, click for source.

The problem: we don’t see this quarterly number until three+ months after the end of a quarter, when the Fed releases its Z.1 report for the the preceding quarter. The Q2 2015 report is due September 18.

But right now we might be able to roughly predict what we’re going to see four+ months from now, in the report on our current quarter, Q3, which ends September 30. We’re a bit over a month from the end the quarter, and we have some numbers to hand.

The U.S. equity markets are down roughly 7% year-over-year (click for source):

Screen shot 2015-08-26 at 11.42.32 AM

Total U.S. equities market cap one year ago was about $20 trillion:

Screen shot 2015-08-26 at 12.27.32 PM

So a 7% equity decline translates to a $1.4-trillion hit to total market cap, which goes straight to the lefthand (asset) side of household balance sheets, because households ultimately own all corporate equity — firms issue equity, and households own it (at one or more removes); people don’t issue equity in themselves, and firms don’t own people (at least not yet). It’s an asymmetrical, one-way ownership relationship. (Note: yes, the Fed accounts for household net worth on a mark-to-market basis.)

Total household net worth a year ago was $82 trillion. The $1.4 trillion equity decline translates to a 1.7% decline in household net worth.

Meanwhile household liabilities over the last four quarters have been growing at a fairly steady rate just above 0.2% per year. There’s no reason to expect a big difference in Q3.

This suggests a 1.9% decline in household net worth over the last year, based on the equity markets alone. (My gentle readers are encouraged to add numbers for real estate and fixed-income assets.) Add (subtract) 1.5% in inflation over that period, and you’re looking at something like 3.4% decline in real household net worth, year over year.

Unless the stock market rallies by 10% or 15% before the end of September ($2–3 trillion, or 2.5–3.5% of $80 trillion net worth), it’s likely we’ll see a negative print for year-over-year change in real household net worth when the Fed releases its Z.1 in early December of this year. And we know what that means — or at least we know what it’s meant over the last half century.

You heard it here first…

Cross-posted at Asymptosis.

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Predicting Recessions The Easy Way: Monetarists, MMT, And The Money Stock

I have a new post up that has implications for stock-market investment, so I decided to try posting it over at Seeking Alpha, where they’re paying me a few tens of dollars for the post (plus more based on page views — not much luck so far).

The post argues that year-over-year change in Real Household Net Worth has been a great predictor of NBER-designated recessions over the last half century. (It’s either 7 for 7, or 8 for 7, over 50+ years, depending on the threshold you use.) If you were following this measure, you would have gotten out of the market on March 6, 2008, avoiding a 50% drawdown over the next twelve months.

But the post goes farther, offering a somewhat monetarist economic explanation but using total household net worth as the measure of the “money stock.” Short story: if households have less (more) money, they spend less (more). Not exactly a radical behavioral economic assertion.

If you’re wondering how recent days’ market events have caused billions (trillions?) of dollars to “disappear,” and are pondering how to think about that, you might find it an interesting read.

Cross-posted at Asymptosis.

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Noah Smith Notes a Puzzle

Noah smith has a question which I paraphrase as : Interest rates on corporate bonds are very low. The return on capital for business as a whole is quite high. Why isn’t investment very high ?

My thoughts

This is related to average v marginal.
I think it is important to distinguish fixed capital into residential capital (AKA houses) non residential structures and equipment (and software).

The user cost of equipment and software is mostly depreciation. There isn’t any particular reason to expect equipment investment to respond to interest rates nor is there much evidence that it ever has.

Most of the rest of investment is residential. It is not related to the returns reported by Gomme et al — households don’t publish balance sheets or profit and loss statements. The return is partly housing services but also, in large part, expected capital gains. These have declined vastly. Or to put it another way, low current investment is almost entirely low housing investment and has nothing to do with corporate bonds or returns on capital.

The question becomes why aren’t firms building lots of structures ? Here I guess that a lot of it is that much of non residential investment in structures is retail (shopping malls) and office parks near new housing developments. That is very much a complement to residential investment and low (given interest rates) as a result.

But also (here really marginal v average) a lot of the profits are going to financial firms (the legend says business not non-financial business). Their marginal return to new structures is low. Another huge chunk is going to high tech. Their return to structures is low as stressed by Summers

I guess the common theme is that corporate profits and investment don’t have much to do with each other, so the Gomme et al meets Smith puzzle isn’t so puzzling.

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The implications of the child care cost crush for median household income and "shadow unemployment"

by New Deal democrat

The implications of the child care cost crush for median household income and “shadow unemployment”

The other day I showed that there is compelling evidence that the primary reason for the long term decline in the Labor Force Participation Rate in the 25 – 54 age range is the increasing real cost of child care, coupled with stagnant to declining real wages in the lower paying jobs typically taken by the second earner in a two earner household.
Today I have a few more precise graphs, and discuss the implications for median household income and the issue of “shadow unemployment” or “missing workers.

First of all is a graph of the increase in the number of those aged 25-54 who are neither employed nor unemployed, but out of the labor force entirely:

Unfortunately this is not avaiable on FRED, but via the BLS, here are the number of people in that above group who tell the Census Bureau each month that they want a job now:

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WORLD TRADE IS FALLING

The recent stock market fall appears to be in reaction

to weakness in foreign economies, not domestic developments

in the US.

 

WORLD TRADE

 

One measure to watch is world trade.

from December to May world trade volume fell -3.4%.

Interestingly, in the first five months of the 1971

decline trade fell -3.5%, essentially the same as this drop.

The year over year growth rate is 0.4%.  The year over year

change in world trade has only turned negative twice sine 1990,

as far back as this data series goes.  For what it is worth

those two declines also coincided with US recessions.

For now, the critical question is how much of the weak growth

abroad impact US growth. Almost certainly the impact is likely

to be significant.

 

 

 

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