Labor Markets and the Macroeconomy: Theory, Evidence and Policy Implications

Morten RAVN (Professor of Economics, University of Southampton / Professor of Economics, European University Institute Research Fellow, CEPR)

This paper, which I wrote with my colleague Saverio Simonelli, is about trying to understand features of the labor market. The Dunlop-Tarshis observation is often said to be a litmus test of "reasonable" business cycle theories. It is an old idea that dates back to 1938, when Dunlop and Tarshis documented that, for the U.S. economy, hours worked and real wages are nearly orthogonal at business cycle frequencies. What I mean by "nearly orthogonal" is that if we map out hours worked versus labor productivity, we see very little relationship between the two. If you change labor productivity to real wages, you will get the same result, they are orthogonal. This has been reinforced over time, and has been shown to hold true for many European countries, and for the post-war as well as the pre-war period.

This observation can be used as a litmus test for theories about the business cycle, because if you have a theory showing a strong positive or negative correlation between labor productivity and hours worked, you know that the theory cannot be factual.

The observation runs into trouble when it is applied to Keynesian style theories and real business cycles (RBC) models. RBC models suppose fluctuations and aggregate productivity shocks are the main source of input in the business cycle. In an RBC model, productivity shocks cause the labor supply curve to shift so that there is an almost perfect correlation between real wages or productivity and hours worked. This is clearly counterfactual to what the empirical evidence of the Dunlop-Tarshis theory states.

In Keynesian theories too, there are problems. In a Keynesian theory, if you have a sticky nominal wage, you should see a clear negative relationship between the low wage and the amount of hours worked.

What this implies is that a good business cycle theory must be one where there is a decoupling between what goes on with hours worked and what goes on with labor productivity.

There have been many papers that have studied this implication, but they have all been focused on the relationship between productivity and hours worked, under no specific conditions. What this paper does is look at the conditional correlation structures. Although hours worked and labor productivity are orthogonal unconditionally, is that also true conditionally during productivity shocks? The paper looks at the relationship during neutral permanent technology shocks and during investment-specific technology shocks. Then, the paper will look at the shocks' impact on the consumption and investment sectors. Following that, the collected evidence will be compared to traditional economic theories.

It turns out that under conditional structures there is some correlation between hours worked and productivity. This occurs as a result of many different shocks. Additionally, there is a difference in the relationship between hours worked and productivity within the consumption and investment sectors.

The paper uses U.S. quarterly data from the years 1960-2003. Two types of technology shocks, neutral permanent technology shocks and investment-specific technology shocks, were identified using a vector autoregression (VAR) approach and the impact of these shocks on aggregate and sector level variables was examined.

We identified the two shocks assuming that only permanent investment-specific technology shocks can affect the long-run level of the relative investment price and that only permanent investment-specific and permanent neutral technology shocks can affect the long-run level of aggregate labor productivity. Having identified the shocks, we then estimated their impact on the consumption and investment sectors.

What we found as a result of our research was that with a neutral technology shock, there is a gradual rise in the level of output, a sudden increase in aggregate hours worked that eventually goes down again, and a gradual rise in aggregate consumption. There is an initially negative impact on investment, but then it goes up again. Aggregate labor productivity shows a bell-shaped response; it goes up upon impact, and then it settles. On the sector level, we found that the hours worked in both sectors go up, although the hours worked in the investment sector go up higher. In the consumption sector, we see a U-shaped impact on labor productivity, while in the investment sector there is a small initial decline.

With an investment-specific technology shock, there is also a gradual rise in output and consumption. A steady state is reached slightly faster than during a neutral technology shock, and there is a greater response in hours worked. Labor productivity, however, looks very different. Initially there is no increase, but in the long run it goes up. At the sector level, we find a much greater impact in the investment sector in hours worked compared to the consumption sector. Across the two sectors there is again a different impact on labor productivity. In the consumption sector there is a U-shaped impact, while in the investment sector we find a rise in labor productivity that grows over time.

Cross-plotting the two sets of data, we see that although there is little or no correlation between labor productivity and hours worked in unconditional circumstances, during an embodied technology shock or neutral technology shock we see very clearly a strong correlation between the two sectors, and this is true across the aggregate, consumption and investment (both in terms of investment in quantities and with relative price adjustments). In the aggregate, there is a negative correlation during a technology shock and a positive correlation during a neutral technology shock. In consumption, where there is actually a slightly negative unconditional correlation, we see negative correlations under both shocks. Looking at the investment sector, measured in quantities, there is a slightly positive unconditional correlation, and it stays positive under the two shocks. With relative price adjustments, the investment sector resembles the aggregate, with no unconditional correlation, a negative correlation during a technology shock, and a positive correlation during a neutral technology shock.

The lesson to be learned is that while the Dunlop-Tarshis observation holds unconditionally, it is not true when measured conditionally in the presence of shocks. It does not hold conditionally at the sector level, and it does not hold conditionally during the two types of technology shocks. At the sector and aggregate level there is a systematic relationship.

Is this consistent with economic theory? We used a business cycle version of the Greenwood, Hercowitz and Krusell 1997 paper to answer this. In addition to the basic assumptions of the model, we assumed that households live eternally, and have rational expectations. Investment goods are those that cannot be consumed, while investment cannot be made in consumption goods. We assume that it is costly to vary the capital and labor inputs. Aggregate output and technology processes are set so that growth in technology leads to growth in output, consumption, investment, capital stocks and relative investment price. We assumed that the capital intensities are identical across the two sectors.

We calibrated a variety of parameters for the models so that they would be consistent with the dynamic effects of technology shocks on sector level variables. These included capital share, growth rates, utility rates and depreciation rates. We estimated, among other things, various elasticities, adjustment costs, and persistent rates of growth.

How does the model do? It accounts well for the impact of the shocks on most aggregate dynamics: output, consumption, investment and hours worked. It is also performs well for investment-specific shocks. It is not successful in terms of fitting the impact on the consumption sector, or hours worked during a neutral shock.

When comparing our model to the U.S. data, it does very well in the aggregate and investment sectors. It does not do well in the consumption sector.

Through all of this, we have reached the following conclusions: (1) While hours worked and productivity are nearly orthogonal at the business cycle frequencies, a conditional correlation structure does not confirm near orthogonality. (2) There are systematic differences across sectors during shocks. (3) Economic theory can account for aggregate evidence very well, but there is still work to do in order to fully account for sectoral evidence.

Q. As far as I remember it is very difficult to get consumption and investment to co-integrate on a nominal level unless you really dig through the category of consumption, what you put into consumption and what you put into investment. Your model implies nominal co-integration, but what did you do to the data to make this property satisfied?

I am not sure why you estimate this model. I think you could do a very simple exercise here and take the neutral and investment-specific shocks you got from your VAR, feed it into your model with some reasonably calibrated parameters and calculate the correlation between the variable of interest conditional to shocks on average. I am not sure that an estimation step here is needed to show what the model can do.

Morten RAVN
Why do we estimate? Because I have no idea what some of these values should be, and I think that if you tried to set a value for some of them you would get a lot of disagreement. You could probably ask about what is the Frisch elasticity and what is the intertemporal elasticity of substitution. However, at least on the Frisch elasticity, there is a lot of disagreement among people. For the adjustment costs, I do not know how I would calibrate them, but they are crucial here. If I put them to zero, the model would not work. Their size is crucial, but the estimates for them are quite different.

Q. You could take the conditional values and compute your technology shock and compare the time path of the technology shock that you obtained here with the one that you obtained with the VAR.

Morten RAVN
I could not do that without knowing things like the adjustment. Conditionally, I could use these estimates and do an account for factual analysis.

Q. The way you have presented the model made it sound like these two shocks are the only shocks. In your empirical model that is not true. There are a number of shocks you have left unidentified, and you have not told us that those are unimportant. If those are the dominant shocks, then the argument you have made becomes uninteresting. I think this is something you need to make clear.

Morten RAVN
We have a purely empirical paper we published last year where we identified two more shocks: monetary policy shocks and government policy shocks. Together, those four shocks account for something like 50%-60% of regulations. For the U.S. economy, monetary shocks are not important. It would be nice to have a model with some nominal frictions, but I did not do that here because it would be difficult.

Q. You could aggregate the remaining shocks without trying to identify them.

Morten RAVN
I could do that but it would not be fair because I do know that the conditional correlation structures for the monetary and government policy shocks are quite different. Clearly other shocks do have an effect, but the two technology shocks account for a sizable portion of the volatility.

Q. How are your results subject to the Fernald critique? When you specify the VAR, you have two variables that show some positive correlation at low frequencies. Fernard has shown where this may influence the estimates of the short run responses to shocks as well.

Morten RAVN
As for the Fernand critique, the fact that we allow from some segmentation in the trends allows us to deal with that. Without segmentation it is not true, and so there needs to be further work on this matter. However, segmentation does partly address the Fernard critique, with breaks in trends and so forth.