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.