Types of unemployment

For economists

This post completes a discussion of a new paper by Pascal Michaillat and Emmanuel Saez. My earlier post outlined their initial model that just had a goods market with yeoman farmers, but with search costs in finding goods to consume. Here I want to look at their main model where there are firms, and a labour market as well as a goods market.

The labour market has an identical search structure to the goods market. We can move straight to the equivalent diagram to the one I reproduced in my previous post.

The firm needs ‘recruiters’ to hire productive workers (n). As labour market tightness (theta) increases, any vacancy is less likely to result in a hire. In the yeoman farmer model capacity k was exogenous. Here it is endogenous, and linked to n using a simple production function. Labour demand is given by profit maximisation. Employing one extra producer has a cost that depends on the real wage w, but also the cost of recruiting and hence labour market tightness theta. They generate revenue equal to the sales they enable, but only because by raising capacity they make a visit more likely to result in a sale. The difference between a firm’s output (y) and their capacity (k, now given by the production function and n) the paper calls ‘idle time’ for workers. As y<k, workers are always idle some of the time. So, crucially, profit maximisation determines capacity, not output. Output is influenced by capacity, but it is also influenced by aggregate demand.

Now consider an increase in the aggregate demand for goods, caused by - for example - a reduction in the price level. That results in more visits to producers, which will lead to more sales (trades=output). This leads firms to want to increase their capacity, which means increasing employment. (More employment reduces x, but the net effect of an increase in aggregate demand is higher x, so workers’ idle time falls.) This increases labour market tightness and reduces unemployment.

Here I think the discussion in the paper (bottom of page 28) might be a little confusing. It notes that in fixed price models like Barro and Grossman, in a regime that is goods demand constrained, an increase in demand will raise employment by exactly the amount required to meet demand (providing we stay within that regime). It then says that in their model the mechanism is different, because aggregate demand determines idle time, which in turn affects labour demand and hence unemployment. I would prefer to put it differently. In this model a firm responds to an increase in aggregate demand in two ways: by increasing employment (as in fix price models) but also by reducing worker idle time. The advantage of adding the second mechanism is that, as aggregate demand varies, it generates pro-cyclical movements in productivity. (There are of course other means of doing this, like employment adjustment costs.)

There are additional interesting comparisons with this earlier fixed price literature. In this model unemployment can be of three ‘types’: classical (w too high), Keynesian (aggregate demand too low), but also frictional. This model can also generate four ‘regimes’, each corresponding to some combination of real wage and price. However, unlike the fixed price models, these regimes are all determined by the same set of equations (there are no discontinuities), and are relative to the efficient level of goods and labour market tightness.

For me, this is one of the neat aspects of the model. We do not need to ask whether demand is greater or less than ‘supply’, but equally we do not presume that output is always independent of ‘supply’. Instead output is always less than capacity, just as unemployment (workers actually looking for work) is always positive. One way to think about this is that actual output is always a combination of ‘supply’ (capacity) and demand (visits), a combination determined by the matching function. This is what matching allows you to do. What this also means is that increases in supply in either the goods market (technical progress) or labour market will increase both output and employment, even if prices remain fixed. In Keynesian models additional supply will only increase output if something boosts aggregate demand, but that is not the case here. However, if the equilibrium was efficient before this supply shock, output will be inefficiently low after it unless something happens to increase aggregate demand (e.g. prices fall).

The aggregate demand framework in the model, borrowed from fixed price models, is rather old fashioned, but there is no barrier to replacing it with a more modern dynamic analysis of a New Keynesian type. Indeed, this is exactly what the authors have done in a companion paper. 

The paper ends with an empirical analysis of the sources of fluctuations in unemployment. It suggests that unemployment fluctuations are driven mostly by aggregate demand shocks. (This is also well covered in their Vox post.) This ties in with the message of Michaillat’s earlier AER paper, where he argued that in recessions, frictional unemployment is low and most unemployment is caused by depressed labour demand. What this paper adds is a goods market where changes in aggregate demand can be the source of depressed labour demand, and therefore movements in unemployment.    

Search in the goods market?

For economists

Imagine an economy made up of independent producers, who individually produce some good. Producers each have a fixed ‘capacity’ k of the output they produce. Producers are also consumers, but cannot consume their own good. Instead they search for other goods by visiting other producers. Agents as consumers have a certain demand for goods, which will depend on how much of their own good they sell, as well as some initial endowment of money and the price of goods in terms of money.

Traditionally we ignore the costs for consumers of visiting producers, and we assume that any visit will result in a purchase. As a result, for a given price level, we can have three situations. In the first, aggregate consumption demand is below aggregate capacity (the sum of all k), and producers end up with either unsold goods or idle capacity. In the second, aggregate demand is equal to supply. In the third, aggregate demand is above capacity. In this case we must have rationing of goods.

In this framework output is not always determined by aggregate demand, but only up to some limit. This is not how macroeconomic models typically work - they generally assume output is always equal to aggregate demand. The way New Keynesian models justify this is by assuming that producers can produce above ‘capacity’ (or that they prefer to always have some spare capacity), and that they will be happy to produce above capacity at a given price because they are monopolistic.

A recent paper by Pascal Michaillat and Emmanuel Saez applies the framework of search to the goods market. First, each visit by the consumer is costly (visiting costs) - some of the produced good is ‘lost’ (does not increase utility) as a result. So output (y, the sum of all trades) is greater than consumption (c) because of these visiting costs. Second, a visit may not lead to a trade. Whether it does depends on a matching function, which depends on the ‘tightness’ of the goods market = x, defined as the ratio of visits to capacity. Here is a diagram from their paper.

The consumption demand line is downward sloping, because a larger number of visits raises the effective price of the produced good. The output line is upward sloping, because more visits result in more trade, but the matching function is such that it gets steeper with more visits. However if visiting costs are linear in visits, that implies what the paper calls ‘consumption supply’ has this rather odd shape. (Think about the constant capital line in the Ramsey model.) For a given price, the intersection of the consumption demand and supply lines defines equilibrium tightness. Perhaps a simpler way of putting it is that consumers plan the number of visits they need to make given their consumption demand schedule.

Now shift the consumption demand line outwards, by reducing the price. (In a New Keynesian framework, think about the price as the real interest rate.) The line pivots about the x^m point, but output always stays below k. As tightness (number of visits) increases, more resources are used up in failed endeavours to make a trade, and consumption starts falling. Output is always ‘demand determined’, and there is no rationing.

It is still possible to think about different ‘regimes’, because the efficient level of tightness is where consumption is at a maximum. If tightness is below that point, we can say that demand is too low (the price level is too high), and vice versa.

Those familiar with matching models in the labour market will see the connections. Visits are equivalent to vacancies, for example. The key question is whether this transposition to the goods market makes sense, and what it achieves. To quote the authors: “casual observation suggests that a significant share of visits do not generate a trade. At a restaurant, a consumer sometimes need[s] to walk away because no tables are available or the queue is too long.” (What is it with economists and restaurants?!) We could add that this rarely means that consumption is rationed - instead the consumer attempts to make a similar trade at another restaurant. However this does have an opportunity cost, which this model captures.

In a subsequent post, I will look at their full model which has separate goods and labour markets, and the various types of unemployment that this can generate. Those that cannot wait can read their own account on Vox.

  

Aggregate demand and the labour market

I’m surprised I do not see a diagram like this more often:

The black lines are familiar from any introductory macro textbook. There is a labour supply curve. It is drawn such that a higher real wage encourages more labour supply, but I will consider what happens if it is vertical later. What I call the ‘unconstrained labour demand’ curve is what firms would choose to do if (a) labour gets less productive as output increases (which is why the curve slopes downward), and (b) firms can sell whatever they like. This is the classical model, and you will find this diagram in nearly every introductory textbook. With flexible wages the level of employment is determined at the intersection of the two curves, and we could call it the ‘natural’ employment level.

However (b) is a fiction. No (surviving) firm produces what it wants to, irrespective of whether people want to buy its product. Aggregate demand can diverge from the level of output implied by the intersection of the two black curves for all kinds of reasons: Says Law does not hold. For simplicity, suppose the aggregate demand for goods in the economy is independent of the real wage, and there is no factor substitution. In that case employment is determined by my red line - it is determined only by aggregate demand. This is pretty clear in the case that I have drawn, where we have deficient aggregate demand. Firms produce what they can sell: they would like to sell more, but there is no point producing more if no one wants to buy more.

It is less clear what happens if the red line shifts right until we have excess aggregate demand. If the number of firms is fixed, why would they produce more than they want to - i.e. at a level where they are losing money on the extra products they are producing? In New Keynesian models where firms are monopolistic and prices are sticky they will produce more if excess demand is modest, because for given prices it is profitable to produce more up to some limit. But will firms be prepared to pay higher (e.g. overtime) wages to workers for long, or will workers be prepared to work more for unchanged wages for long? I will come back to this at the end.

If there is deficient demand, is there anything that makes the red line move right to achieve the natural employment level? With deficient demand, prices may tend to fall, but that alone is unlikely to shift the red line to the right: few people talk about Pigou effects anymore, and the general concern is that deflation is deflationary because the real value of debt has increased. It is monetary policy that shifts the red line in the required direction, either because it responds to falling prices or because it wants to reduce the output gap. Ironically, Real Business Cycle models, which assume the red line is always at the natural employment level, only make sense in a world where monetary policy is very efficient. However, monetary policy does normally work over the medium term, which is why the classical or RBC model makes sense if we are just doing medium/long term analysis.

What happens to the real wage? In the most basic of New Keynesian models, the labour market clears, which means real wages fall until the labour supply curve intersects the red line. (Here a vertical supply curve would be a problem.) If, in contrast, real wages were sticky, we would get involuntary unemployment - rationing in the labour market. Which is true matters a great deal to those unemployed, but it terms of modelling deviations from the natural rate the difference is not that great. Real wages have no direct impact on aggregate demand, and so all that might happen is that monetary policy could be influenced one way or the other. If it is not, what happens to real wages is irrelevant to the basic problem, which is deficient aggregate demand. This is one reason why New Keynesian economists may be happy to work with a model where the labour market clears, but there may be other reasons.

The vertical red line assumes no factor substitution. With factor substitution it can become downward sloping: falling real wages lead firms to substitute labour for capital, which can increase employment even if output is unchanged because aggregate demand is unchanged. As I speculate in this post, based on the work of Pessoa and Van Reenen, something like this could help explain the current UK productivity puzzle. If this speculation is correct, at some point as aggregate demand and investment expands real wages will rise, and labour productivity will increase as factor substitution is reversed.

I was prompted to write this post by this from Noah Smith, which in turn comments on a post by John Quiggin. (See also Mike Konczal and Nick Rowe.) They talk about models of labour market matching, which I have not mentioned, but similar considerations apply with matching models taking the place of the classical model (although there are key differences between the two). This gives me another chance to plug an AER paper by Pascal Michaillat, which addresses the possible asymmetry that may occur when we have excess demand. Michaillat’s model is a matching model when aggregate demand is strong, but a rationing model (with Keynesian involuntary unemployment) when aggregate demand is low. This is one, rather interesting, answer to the question I asked above about possible asymmetry. Putting matching together with Keynesian rationing is complicated, but if Michaillat’s paper is ignored just for this reason, that says something rather sad about current macro methodology. 

New Keynesian models and the labour market

Do all those using New Keynesian models have to believe everything in those models? To answer this question, you have to know the history of macroeconomic thought. I think the answer is also relevant to another frequently asked question, which is what the difference is between a ‘New Keynesian’ and an ‘Old Keynesian’?

You cannot understand macro today without going back to the New Classical revolution of the 1970s/80s. I often say that the war between traditional macro (Keynesian or Monetarist) and New Classical macro was won and lost on the battlefield of rational expectations. This was not just because rational expectations was such an innovative and refreshing idea, but also because the main weapon in the traditionalists armoury was so vulnerable to it. Take Friedman’s version of the Phillips curve, and replace adaptive expectations by rational expectations, and the traditional mainstream Keynesian story just fell apart. It really was no contest. (See Roger Farmer here, for example.)

I believe that revolution, and the microfoundations programme that lay behind it, brought huge improvements to macro. But it also led to a near death experience for Keynesian economics. I think it is fairly clear that this was one of the objectives of the revolution, and the winners of wars get to rewrite the rules. So getting Keynesian ideas back into macro was a slow process of attrition. The New Classical view was not overthrown but amended. New Keynesian models were RBC models plus sticky prices (and occasionally sticky wages), where stickiness was now microfounded (sort of). Yet from the New Classical point of view, New Keynesian analysis was not a fundamental threat to the revolution. It built upon their analysis, and could be easily dismissed with an assertion about price flexibility. Specifically NK models retained the labour leisure choice, which was at the heart of RBC analysis. Monetary policymakers were doing the Keynesian thing anyway, so little was being conceded in terms of policy. [1]

So labour supply choice and labour market clearing became part of the core New Keynesian model. Is this because all those who use New Keynesian models believe it is a good approximation to what happens in business cycles? I doubt it very much. However for many purposes allowing perfect labour markets does not matter too much. Sticky prices give you a distortion that monetary policy can attempt to negate by stabilising the business cycle. The position you are trying to stabilise towards is the outcome of an RBC model (natural levels), but in many cases that involves the same sort of stabilisation that would be familiar to more traditional Keynesians.

This is not to suggest that New Keynesians are closet traditionalists. Speaking for myself, I am much happier using rational expectations than anything adaptive, and I find it very difficult to think about consumption decisions without starting with an intertemporally optimising consumer. I also think Old Keynesians could be very confused about the relationship between aggregate supply and demand, whereas I find the New Keynesian approach both coherent and intuitive. However, the idea that labour markets clear in a recession is another matter. It is so obviously wrong (again, see Roger Farmer). So why did New Keynesian analysis not quickly abandon the labour market clearing assumption?

Part of the answer is the standard one: it is a useful simplifying assumption which does not give us misleading answers for some questions. However the reason for my initial excursion into macro history is because I think there was, and still is, another answer. If you want to stay within the mainstream, the less you raise the hackles of those who won the great macro war, the more chance you have of getting your paper published.

There are of course a number of standard ways of complicating the labour market in the baseline New Keynesian model. We can make the labour market imperfectly competitive, which allows involuntary unemployment to exist. We can assume wages are sticky, of course. We can add matching. But I would argue that none of these on its own gets close to realistically modelling unemployment in business cycles. In a recession, I doubt very much if unemployment would disappear if the unemployed spent an infinite amount of time searching. (I have always seen programmes designed to give job search assistance to the unemployed as trying to reduce the scaring effects of long term unemployment, rather than as a way of reducing aggregate unemployment in a recession.) To capture unemployment in the business cycle, we need rationing, as Pascal Michaillat argues here (AER article here). This is not an alternative to these other imperfections: to ‘support’ rationing we need some real wage rigidity, and Michaillat’s model incorporates matching. [2]

I think a rationing model of this type is what many ‘Old Keynesians’ had in mind when thinking about unemployment during a business cycle. If this is true, then in this particular sense I am much more of an Old Keynesian than a New Keynesian. The interesting question then becomes when this matters. When does a rationed labour market make a significant difference? I have two suggestions, one tentative and one less so. I am sure there are others.

The tentative suggestion concerns asymmetries. In the baseline NK model, booms are just the opposite of downturns - there is no fundamental asymmetry. Yet traditional measurement of business cycles, with talk of ‘productive potential’ and ‘capacity’, are implicitly based on a rather different conception of the cycle. A recent paper (Vox) by Antonio Fatás and Ilian Mihov takes a similar approach. (See also Paul Krugman here.) Now there is in fact an asymmetry implicit in the NK model: although imperfect competition means that firms may find it profitable to raise production and keep prices unchanged following ‘small’ increases in demand, at some point additional production is likely to become unprofitable. There is no equivalent point with falling demand. However that potential asymmetry is normally ignored. I suspect that a model of unemployment based on rationing will produce asymmetries which cannot be ignored.

The other area where modelling unemployment matters concerns welfare. As I have noted before, Woodford type derivations of social welfare give a low weight to the output gap relative to inflation. This is because the costs of working a bit less than the efficient level are small: what we lose in output we almost gain back in additional leisure. If we have unemployment because of rationing, those costs will rise just because of convexity. [3]

However I think there is a more subtle reason why models that treat cyclical unemployment as rationing should be more prevalent. It will allow New Keynesian economists to say that this is what they would ideally model, even when for reasons of tractability they can get away with simpler models where the labour market clears. Once you recognise that periods of rationing in the labour market are fairly common because economic downturns are common, and that to be on the wrong end of that rationing is very costly, you can see more clearly why the labour contract between a worker and a firm itself involves important asymmetries - asymmetries that firms would be tempted to exploit during a recession. 

Yet you have to ask, if I am right that this way of modelling unemployment is both more realistic and implicit in quite traditional ways of thinking, why is it so rare in the literature? Are we still in a situation where departures from the RBC paradigm have to be limited and non-threatening to the victors of the New Classical revolution?

[1] When, in a liquidity trap, macroeconomists started using these very same models to show that fiscal policy might be effective as a replacement for monetary policy, the response was very different. Countercyclical fiscal policy was something that New Classical economists had thought they had killed off for good.

[2] Some technical remarks.

(a) Indivisibility of labour, reflecting the observation (e.g. Shimer, 2010) that hours per worker are quite acyclical, has been used in RBC models: early examples include Hansen (1985) and Hansen and Wright (1992). Michaillat also assumes constant labour force participation, so the labour supply curve is vertical, and critically some real wage rigidity and diminishing returns.

(b) Consider a deterioration in technology. With flexible wages, we would get no rationing, because real wages would fall until all labour was employed. What if real wages were fixed? If we have constant returns to labour, then if anyone is employed, everyone would be employed, because hiring more workers is always profitable (mpl>w always). What Michaillat does is to allow diminishing returns (and a degree of wage flexibility): some workers will be employed, but after a point hiring becomes unprofitable, so rationing can occur.  

(c) Michaillat adds matching frictions to the model, so as productivity improves, rationing unemployment declines but frictional unemployment increases (as matches become more difficult). Michaillat’s model is not New Keynesian, as there is no price rigidity, but there is no reason why price rigidity could not be added. Blanchard and Gali (2010) is a NK model with matching frictions, but constant returns rules out rationing.

[3] I do not think they will rise enough, because in the standard formulation the unemployed are still ‘enjoying’ their additional leisure. One day macroeconomists will feel able to note that in reality most view the cost of being unemployed as far greater than its pecuniary cost less any benefit they get from their additional leisure time. This may be a result of a rational anticipation of future personal costs (e.g. here or here), or a more ‘behavioural’ status issue, but the evidence that it is there is undeniable. And please do not tell me that microfounding this unhappiness is hard - why should macro be the only place where behavioural economics is not allowed to enter!? (There is a literature on using wellbeing data to make valuations.) Once we have got this bit of reality (back?) into macro, it should be much more difficult for policymakers to give up on the unemployed.

References (some with links in the main text)

Olivier Blanchard & Jordi Galí (2010), Labor Markets and Monetary Policy: A New Keynesian Model with Unemployment,  American Economic Journal: Macroeconomics, vol. 2(2), pages 1-30

Hansen, Gary D (1985) “Indivisible Labour and the Business Cycle” Journal of Monetary Economics 16, 309-327

Hansen, Gary D and Wright, Randall (1992) “The Labour Market in Real Business Cycle Theory” Federal Reserve Bank of Minneapolis Quarterly Review 16, 2-12.

Pascal Michaillat (2012), Do Matching Frictions Explain Unemployment? Not in Bad Times, American Economic Review, vol. 102(4), pages 1721-50.

Shimer, R. ‘Labor Markets and Business Cycles’, Princeton, NJ: Princeton University Press, 2010.