## Saturday, May 3, 2014

### Why Participation Is Down

There have been many attempts to answer this question: Is the decline in the U.S. labor force participation rate structural or cyclical? Or, more precisely, to what extent is it either one?

And there have been so many attempts because it really is an important question. Think about the economy as a big machine that takes three inputs -- technology, labor, and capital -- and produces output. The drop in the labor force means that the U.S. has forfeited, perhaps permanently, that labor input and whatever marginal output it would have yielded. A simple calculation1 suggests that the share of output lost is about three percent; more in-depth calculations from Reifschneider, Wascher, and Wilcox (2013) place it at the center of their estimate of a seven-percent drop in potential output. That's a lot. You don't blow three percent of GDP, let alone seven, every day.

Another reason that economists keep coming back to the labor force participation rate is that, ominously, it keeps falling. Not only does that render much of the research overtaken by events, but also the data presents a challenge to reports that see the decline as cyclical and transitory.

I'd also say that the reason that the research continues2 is because it hasn't settled on a single analytical framework. That's not necessarily a bad thing at all, as disagreement over methods forces researchers to reconcile differences in results rather than herd around a single conclusion. Yet to a certain degree it reflects dissatisfaction with the methods offered so far.

In this post I take an approach that is mostly3 new to the question of the decline in the labor force participation rate but will be familiar to most labor economists, the Blinder-Oaxaca decomposition of a probit model for the labor force participation decision. I use microdata from the March 2007 and 2013 supplements to the Current Population Survey, downloaded from IPUMS. I conclude that, of the 2.8-percentage-point decline in the labor force participation rate over that six-year period, more than half (1.7 percentage points) can be explained by underlying changes in demography, though a substantial fraction (1.1 percentage points) cannot.

The method

For the majority of my audience that has no idea what a Blinder-Oaxaca decomposition is, here's a quick 101. It's a statistical technique invented by Alan Blinder and Ronald Oaxaca in 1973 that takes the change in a variable and determines how much of it can be explained by a set of other variables in a model and how much can't. (Note: What comes next gets rather mathy, but you can skip down to "My idea..." if math isn't your thing.)

For example, Blinder and Oaxaca both wanted to understand why people differ in their earnings. Let's say that you think pay is determined by a bunch of factors, like your education, work experience, occupation, and so on. Let's put all of those factors into a matrix X, which contains data on lots of people. Let's put all of their earnings into another matrix Y. Then we can estimate the impact of all of those factors by an ordinary least squares regression:

Y = Ε

where β is the matrix of coefficients, which reflects the impacts of the factors, and Ε is a matrix of residuals

Now here's the innovation from Blinder and Oaxaca: If we want to understand a change in Y between two periods, then in the context of our model, there can only be two things going on. Either X or β could have changed -- that is, there could have been an underlying change in the determinants X of pay Y, or there could have been a change in the impacts of factors, reflected in β. We can express that idea as:

ΔY = Ya - Yb = (X- Xb)βb + Xa(β- βb)

where the "a" subscripts are for the "after" period and the "b" subscripts for the "before" period. You can think of the first term as the explained share, changes in the composition of the independent variables. And you can think of the second term as the unexplained share, changes in effects.

Now, my application of this model is a little bit more complex, because we're trying to explain a binary variable. "Are you in the labor force?" can get an answer of yes or no. So I've used something called a probit model, which allows us to estimate the probability that you answer yes or no to that question, given your characteristics. Our changes in the probabilities can also be divided in just the same way into changes in characteristics and changes in the effects of characteristics.

These techniques might seem exotic or advanced to newcomers. To economists, though, they're standard practice. So much so that it's surprising that I was not able to find a single piece of research that did what I think should be the first cut at answering this oh-so-important question about the decline in labor force participation.

My idea, to be sure, was pretty simple. Here, I'll explain it without the math. Create a model that includes everything you think might be relevant to the decision of whether to participate in the labor force or not. Find data on an "after" period (March 2013) and a "before" period (March 2007). Then see what change in the labor force participation rate the model predicts. But, whatever you do, don't tell the model that a recession happened between 2007 and 2013. Include everything you think might explain the labor force participation decision in a structural capacity -- but nothing else.

My dataset is the March 2007 and 2013 supplements to the Current Population Survey. That gives me a sample size of roughly 150,000 people for both years. To predict whether or not each of these people are in the labor force, I had data on lots of different things: their age, sex, race, marital status, health status, disability status, education, whether they are currently enrolled in school, whether they're a war veteran, whether they have young children at home, and whether they're on welfare.

It turns out that all this information is enough to make a good guess at whether you actually are in the labor force or not. On average, the model gets it right 81 percent of the time, assuming that you think of predictions of 50 percent and above as a "yes" and below 50 percent as a "no."

And I've deliberately gone out of my way to include common narratives about why the labor force participation rate has fallen. The aging and retirement of the Baby Boomers. The rise in worker disability. The rise in college enrollment. Furthermore, the unexplained share of this method will identify the specific areas of unexplained changes -- for instance, if women en masse suddenly have decided to stop working (and it turns out they haven't), this method will point at that issue. So one of the huge advantages to this approach is that it allows us to do a bunch of tests of specific theories one-by-one and say whether they hold water or not.

The results

The headline result is that 1.7 percentage points of the decline in the labor force participation rate are explained by changes in the demographic composition of the population, and that 1.1 percentage points are left unexplained. The 95-percent confidence intervals on those figures are that between 1.4 and 1.9 percentage points are explained and between 0.8 and 1.4 percentage points are unexplained.

This is a good place to note that I've made my .do files available here, so that you can go home and replicate this work, as I know you're all dying to do.

What matters to explaining the decline in the labor force participation rate? One thing above all else: aging, which explains 1.3 percentage points of the drop. The next most important: enrollment in school, which explains 0.8 percentage points of the drop. Remember that individual explanations can sum to more than the total, because there are other changes that partially offset. For example, the rise in educational attainment, which comes from this enrollment, explains a 0.6 percent rise in the labor force participation rate, because the well-educated work like crazy.

What matters less? The rise of disability, which explains 0.2 percentage points of the drop. The decline in the birthrate during the recession, which would suggest a 0.1-percentage-point increase, since fewer people are tied down at home with four-year-olds.

And what just straight up doesn't matter? Changes in the share of people on welfare, disability aside. Changes in health, after accounting for disability and age. Changes in the sex and race composition of the labor force.

It also turns out that there's no single category that absorbs most of the unexplained share. In fact, the model puts almost all of the unexplained share into a constant. Which basically means that the model is saying, "Whatever your background, take what your probability of being in the labor force was in 2007 and mark it down by some amount for your 2013 probability." I found this compelling evidence that what our model says is unexplained really is the business cycle, and not some omitted structural explanation.

Here, also, is maybe a conclusion you wanted: What does the model predict the labor force participation rate is in March 2013 based on these changes in composition? 64.7 percent, as compared to an actual rate of 63.5 percent. Perhaps this makes you view my conclusion differently, if "less than half cyclical" sounded dour. This wouldn't be a trivial amount of recovery, as you can see in this graph. The black dot not on the line indicates the March 2013 counterfactual.

Conclusion

I've been meaning to write a post on this for a long time. It is the analytical challenge of our era for economists. It's taken me so long to put together an estimate because I wanted an approach I could defend.

One valuable side note is that the change in the working-age labor force participation rate is probably a good rule of thumb for the change in the overall structural labor force participation rate. The drop is about the same as predicted. Which makes sense: These are people whose labor force decision should not be sensitive to the business cycle. They're in the working period of their lives.

I should also mention some shortcomings of this analysis. One of them is that I've only used data from two months, the March 2007 and 2013 CPS supplements. This was mainly out of convenience, as that was the data available on IPUMS, the database I linked to earlier.

Another concern is the obvious endogeneity problem with education. That is, if the economy's terrible, that affects your decision of whether to work now or to go back to school. But note that this problem is insoluble without a model of how the economy affects education decisions, something well beyond the scope of my work here. What my work suggests, though, is that this exercise is worthwhile. Since you get a year older every year, there's not a lot of mystery to the aging-working link. But, since we know now that education decisions were actually important to driving down overall labor force participation, maybe we should go back and think about it carefully.

A final concern is that a lot of the prior research I looked at includes what are called "cohort effects," that is, you think about labor force participation evolving differently for different generations of people, based on their pre-recession starting age. I don't do that in this model. If cohorts matter, this approach will miss it.

Part of my hope of writing this post, whether or not you agree with the overall conclusion, is to enlighten people about the explanatory power of all the theories on the table. If you're on the right, and walk away from this post saying, "Gosh, I wasn't convinced that the decline in the labor force participation rate is partly cyclical, but wow, maybe it really isn't all about more people on welfare," I'll take that as a victory. Or, if you're on the left, and think, "Gosh, I wasn't convinced that the decline in the labor force participation rate is more than half structural, but wow, maybe aging is a bigger part of the story than I thought," I'll also take that as a victory. And, for sure, this won't be the last word. There are many other compelling approaches, each with their advantages and disadvantages. But I think this is an important one that needs to be added to the conversation.

If you have questions, I'm happy to answer them in the comments.

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1. Assume that GDP is described by a Cobb-Douglas aggregate production function with a labor share of 0.6, consistent with U.S. levels. Then, holding capital and technology constant, you would predict that a 5-percent drop in the labor force participation rate would cause a 3-percent drop in output.

2: You can find a good literature review in Erceg and Levin (2003).

3: There is an exception, Hotchkiss and Rios-Avila (2013). But it does something I think is not good, which is that it includes a measure of labor-market conditions. My approach differs importantly in that I don't include one because I want to see the conclusions of the model without telling it about the recession. I have some other concerns about the particular measure they've chosen and whether we really can include it in the model if it is codetermined with labor force participation.

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Further results:

Alan Reynolds of the Cato Institute asked me to try repeating the decomposition with broader measures of welfare programs -- the one I used originally was narrow, i.e. TANF, and Reynolds wanted SNAP (food stamps), Medicare, and Medicaid.

Following other ideas in the comments, I also included cubic and quartic terms in the age, so as to better approximate the curve of the LFPR in the cage. I found that inclusion of the extra age terms didn't do much.

I found that the increase in the fraction receiving public health insurance was an important explanatory variable for the decline of the labor force participation rate: It explains about 0.6 percentage points. I found the increase from SNAP was rather small: It explains 0.2 percentage points. In the new specification, fully 2.5 percentage points of the 2.8 percentage point from in the LFPR is explained by changes in the composition of the workforce.

I would strongly caution Alan, or anyone really, from interpreting this as a causal result. Don't conclude that because Obama expanded Medicaid and food stamps, those new recipients aren't working any more. I imagine that most of this growth was the result of the business cycle. The causal pathway probably goes from unemployment to those programs. I am aware Medicaid expanded permanently, but there is no way to disentangle this.

1. Evan,

Great work! My time studying econometrics may have made me a little bit of a snob for careful statistics, so a few technical comments.

1. Matrix multiplication is not commutative, so you should keep the betas on the same side when writing out the decomposition.

2. I think you should see if you can cluster the standard errors by time, and by state at the minimum. Your observations are all correlated with each other in each cross section, and you should try to reflect that in your model.

3. Probit assumptions tend to be much more restrictive than OLS. In particular, they do not give even consistent estimates in the presence of heteroskedasticity. See: http://davegiles.blogspot.com/2013/05/robust-standard-errors-for-nonlinear.html

4. Time series are a black magic. (That is perhaps the most substantive conclusion I have gleaned from reading Hamilton). I suspect something will be very weird if you play with the assumptions on the generating process even for the dependent variable (AR? Unit root?). As motivation, I think your approach is equivalent to one big regression on the pooled dataset (both years) of:

Labor Force ~ (Year Dummy) [interact with] (All regressors)

And your decomposition result is just "what would the model predict if the year dummy was set for 2013 but the regressors changed" for your structural effect (\beta_b * (Xa - Xb)), and "what would the model predict if we fixed the regressors in 2007 and changed the year dummy?" for your cyclical effect.

But if this is indeed your regression, the extent to which your observations are correlated would likely have a massive effect on your standard errors. Another intuitive way to see this is that if you wanted to see how rainfall in two cities affected crop yields, your standard error from regressing yields for the farmers in the two cities on the rainfall in the two cities would be too small. You're not really observing 1000's of farmers, you're really just observing two cities and their weather.

For more, you can take a look at the classic Moulton paper on state-level regressors in employment. A short answer problem based on this paper actually showed up on my final exam a few days ago.

5. I would be interested in using some data mining techniques to see if we can get more insight out of this. I just took a class on these kinds of methods, and I think they would help the exposition quite a bit (for example, we could put the year dummy in as an explanatory variable and see how "important" it is in a tree classification model). For more, see: http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.28.2.3.

6. Could you put up a public dropbox link for the data files somewhere?

These are just a few of my thoughts. You always have been very talented at finding the pressing questions to address and applying standard econometric techniques, and this post is more evidence of that. Keep it up.

1. 1. Good catch. I was working off some notes which didn't use matrices.

2. Generally speaking, you need many clusters for clustering to make sense. (Usually, the rule is > 50.) I have two time periods, so clustering by time isn't going to work. Clustering by state is more interesting, but I can't think of a reason to think intrastate decisions are going to be correlated. I would want to cluster by id, but the CPS isn't a panel dataset.

3. Aware of that. I checked this earlier. Heteroskedasticity is significant statistically but not at all in a "does it change your results" way. I estimated a heteroskedasticity-consistent probit model (hetprob in Stata) and get basically the same model. Also the same from Blinder-Oaxaca if you do LPM.

4. I'm not quite sure what you're going at here. This is a highly standard approach.

5. I haven't learned that type of modeling yet. Next year, I think.

6. http://www.filedropper.com/cps00006.

Thanks!

2. Undergrad here. I've run regressions on the Census recently, and have tried to find out how cluster errors appropriately. A few points to add to what Yichuan Wang has said:

1. On clustering errors by state:
Differential tax policy and social safety nets can affect the labor force participation rate, so we should expect correlation of labor force status between observations in the state. Regional business cycles/trends might also be responsible for this.

2. Clustering by survey sampling units:
You might want to svyset the data and use the svy prefix for an alternative way of clustering errors with pooled cross-sections. See http://www.stata.com/statalist/archive/2011-09/msg01244.html. If my understanding is correct, the discussion there indicates that standard errors will still be too large with this method when the sampling units are the same across time.

3. You might also want to try running your regression on census and ACS data. You'll probably have a bigger problem of "too small" standard errors because the sample size is that much larger. Also, note that the sampling is different so you have to drop observations accordingly. IIRC, the census includes people in institutional quarters (e.g. correctional facilities).

3. Hi, undergrad. Welcome to the club.

I'll test out your clustering points soon, hopefully. And yes, it would be a good idea to compare my results to what I get from Census and ACS data.

Thanks for the ideas.

4. Heteroskedasticity adjustments for linear regression usually just change the standard errors, rather than the coefficients. I can't recall if that is also true for models like probit. Anyway, Wang's point is about serial correlation, not heteroskedasticity.

5. Yes, heteroskedasticity makes the OLS estimator inefficient but does not affect consistency. In the probit, heteroskedasticity does lead to inconsistency.

2. What you and pretty much all economists fail to do is consider the lack of demand.

Seems to me the refusal to hire workers and the refusal to pay wages high enough to pay the cost of being a worker is a signal to workers they should not be workers.

Why don't you explore the reasons for the lack of buggy whips and buggy whip makers. Is this a structural problem in the buggy whip sector. Are buggy whip makers demanding wages that are too high? If buggy whip makers would accept a job at $1 per hour would industry hire more buggy whip makers? If it the Democrats who caused the falling employment of buggy whip makers by raising the minimum wage to$7.25? Is it Obamacare? The aging of the boomers? The pollution rules that banned horses from the cities?

If we look at buggy whip maker employment in the larger context we understand that pollution and labor cost were big drivers in the demise of those jobs because a labor saving alternative that relied on labor saving burning of natural capital - fossil fuel - allowed for more people and labor in denser cities. Fortunately the reduction in labor needed for horse power replaced by burning capital was offset by the need to build capital assets - roads, bridges (because cars were not as flexible as horse and oxen), water and sewer (high density population vs rural distributed supply and disposal), etc.

What I see workers responding to the signals the economists have been urging be sent: focus on cutting jobs to boost profits, focus on cutting wages to boost profits, focus on cutting labor by automation to boost profits, use existing capital more intensively to cut jobs building new capital to boost profits.

No economist I see is saying, "we need to give consumers more money to spend by increasing wage rates and building more capital assets using abundant profits to create jobs and drive up wages because only when consumers have more money will they buy more consumer and capital to boost economic growth. which will increase demand for labor.

And by the way, given we lack no shortage of labor, why are we burning capital when we have the labor to build energy capital: solar and wind harvesting capital and the capital to distribute and store it and use more of it instead of fossil fuels?

If economists call for more burning of natural capital, then they are effectively calling for reduced labor demand, which means paying lower wages, which means less consumer demand,...

1. You say that: "No economist I see is saying, "we need to give consumers more money to spend by increasing wage rates and building more capital assets using abundant profits to create jobs and drive up wages because only when consumers have more money will they buy more consumer and capital to boost economic growth. which will increase demand for labor."

Almost every economist I know is saying this.

3. Nice post, Evan. I think it would have been helpful to set your findings a bit within the literature - how does your approach lead to results that differ from others out there? what does your method add?

I still think the interpretations are delicate regardless of the estimator. Some (most?) of the "demographics" may have been influenced by the recession (particularly such a large one). I know you mentioned education but I think it is worth noting again. For example, here's a relevant excerpt from Aaronson et al (2006) http://www.brookings.edu/~/media/projects/bpea/spring%202006/2006a_bpea_aaronson.pdf when they are look at the 2000-05 decline in LFPR: "Nevertheless, the fact that enrollment itself responds cyclically makes distinguishing the long-run from the cyclical influences on participation more difficult." College enrollments rose considerably after this recession too -- and that almost certainly has to be linked in part to the cycle. Disability probably has some similar dynamics, and delayed retirement (in the other direction). If I understand correctly you do not use any business cycle indicators, much less interact them with demographics. This strikes me as an important omitted variable.

I know the Aaronson et al model (a cohort-style) is different than yours but I think it shows how tough making predictions from such estimation is. If you look at Figure 12 in their paper, they were quite close in 2006 to predicting the lower level of the LFPR in 2014, but they were not including the Great Recession in their model projection. So it seems possible that models using historical trends could actually give 'too much' weight to structural changes. I too would be skeptical of results that say the LFPR decline is all structural or all cyclical, especially as the cyclical/structural decomp is getting harder to do as the recovery stretches on - still the magnitudes are important.

All this is not to discourage from your exercise, but it does seem crucial to look at subcomponents and think about how they might change under different demand conditions.

1. Claudia, thanks for commenting. Your perspective is super valuable to me. Re a lit review, yes, I should have one. I'm saving that for when I turn this post into a published paper.

I agree completely on the endogeneity issue with college enrollment and possibly disability. The reason they were included was because I wanted to evaluate how much they've pushed down LFPR if treated as exogenous, not because I really believe them to be so. What this analysis tells us, then, is that the college thing is actually important quantitatively in the aggregate data, even relative to aging.

The delayed retirement phenomenon will show up as an unexplained change in coefficients, so there's a good application of the decomposition results for you. More generally, all this stuff will show up in unexplained coefficients, which is an additional motivation for this analysis, because we identify the specific areas of unexplained changes.

The reason I omit business cycle indicators is because I'm not sure I can even do that -- if I think LFPR is codetermined with it, isn't that problematic? I have to think about this more. It seems to me that the proper way to think about it is all the Xs as demographic variables. After all, I only have two periods -- any business cycle stuff is going to be a time fixed effect, which I capture in my constant anyway, or is going to already have interactions in the unexplained part.

4. I'm curious as to whether you included any dummy variables for age (i.e. 1= over 65) as to my knowledge, the way a probit interacts with a continuous variable would would overfit the middle of the distribution and underfit the top and bottom, thus not compensating sufficiently for the drop-off one might expect for retirement aged workers.

Otherwise, incredibly lucid explanation of a probit, and the description of Oaxaca Blinder was really helpful.

1. Thanks.

The way I dealt with age is a standard approach in labor econometrics. I have a continuous age variable, and a variable for the square of the age. In a wage function, this would allow us to think of the wage as quadratic in the age, which is a good approximation.

I did the same thing here. If you think about the consequence of that assumption, it means that the LFPR should form an approximately normal (i.e. Gaussian) curve with respect to age. (This is exactly true, and generally easier to see, if you think about my model as a logit, not a probit.) It turns out (and I'm just looking into this now, so thank you for your comment) that this is a decent assumption. I think a better idea might be to fit a quartic. That's also pretty common in the labor research: http://scholar.google.com/scholar?hl=en&q=quartic+wage&btnG=&as_sdt=1%2C31&as_sdtp=.

2. Sorry, forgot a link for the age curve of the LFPR: http://www.clevelandfed.org/research/Trends/2008/0808/03ecoact-2.gif. The motivation for a quartic would be to better capture the "flat top" and "fast drop" phenomena we see in the chart.

5. I'd like focus on a couple of broad questions.

Whether structural or cyclical, a declining participation rate is a cause of concern. At what level does it become critical?

What is the composition of the structural non-participants? Are the retirees those with hefty 401(k)s or are those who rely heavily on SS? As, are you yourself asked (I think), are the young non-participants continuing education (and presumably adding debt) doing so for lack of employment opportunities?

And given the cyclical component, what impact is likely given the latest flatline quarterly growth and the political unlikelihood of additional significant stimulus?

Laugh about it or shout about it, for the economy to work people have to have money to spend in order to generate demand so that producers have reason to produce. When 40% of the people aren't earning new income there had better be a boatload of dividends and transfer payments floating around to keep them spending or the 'cyclical' component of this will have an awfully long period.

1. 1. I'm not sure if I think about there being some sort of criticality threshold for the problem of the declining LFPR. The reason it is worth watching, though, is mainly because it is hugely relevant to macroeconomic policymaking for the next 5-10 years.

2. The change in structural nonparticipants mostly reflects the aging population and a rise in college enrollment. A little bit of a rise in disability, as well. This is all in the post. The unexplained component is across the board, as I say in the post. The salient unexplained phenomenon is the effect on the constant.

3. I wouldn't rush to any conclusions from one quarter of GDP growth.

4. Generally speaking, economists haven't found it helpful in a very long time to think about the aggregate economy in MPC (marginal propensity to consume) terms, that is, with a Keynesian cross model. That's because it doesn't think about anything in the context of intertemporal equilibrium. Whether you like that or not, that's why the "laugh about it or shout about it" argument you provide has so little traction among economists.

2. "I'm not sure if I think about there being some sort of criticality threshold for the problem of the declining LFPR."

That made me chuckle. I'm inclined to leave it at that.

2. My question was rather more subtle than your answer. "I don't know" or "I don't care" would have been perfectly acceptable. "Can't you read?", not so much.

3. Neither would I. But we do track these things and report them for a reason, don't we? What passes for 'this recovery' has been something less than robust with last quarter serving as sort of a poster child.

4. "[E]conomists haven't found it helpful in a very long time to think about the aggregate economy in MPC (marginal propensity to consume) terms..." Perhaps not. But many of the people whose behavior economists claim to model do think in just those terms. Does theoretical economics without translational application rise above masturbation?

6. A thought: you identify unexplained variables as "cyclical." Is that really appropriate? I mean, let's imagine a hypothetical world where the became a pacifist nation between your two time periods and laid off every soldier. This would probably cause some kind of blip which might have relatively little correlation with your demographic controls, but it wouldn't be proper (I think) to call it "cyclical."

That is, wouldn't it be proper to say your results suggest that it's probably a bit over half structural, and a bit over half "something else"? And that "something else" MAY be the business cycle... or it could be, well, something else. Policy changes unrelated to welfare seem like an obvious one, but I see no reason technology shocks couldn't be just as relevant. These changes, if uncorrelated with your "structural" variables, could be just as important.

Adding to that, if a policy change or technology shock (or really any kind of shock) has results which ARE correlated with your controls, you could be overstating the structural component. For example: let's imagine a world where the government changed the retirement age between the two periods. This shock would probably alter labor force participation rates, and probably do so in a way that correlated with your "structural" component.