What’s Wrong With Modern Macro? Part 4 How Did a "Measure of our Ignorance" Become the Cause of Business Cycles?

Part 4 in a series of posts on modern macroeconomics. Parts 1, 2, and 3 documented the revolution that transformed Keynesian economics into DSGE economics. This post begins my critique of that revolution, beginning with a discussion of its reliance on total factor productivity (TFP) shocks.

Robert Solow (Wikimedia Commons)
Robert Solow (Wikimedia Commons)

In my last post I mentioned that the real business cycle model implies technology shocks are the primary driver of business cycles. I didn’t, however, describe what these technology shocks actually are. To do that, I need to bring in the work of another Nobel Prize winning economist: Robert Solow.

The Solow Residual and Total Factor Productivity

Previous posts in this series have focused on business cycles, which encompass one half of macroeconomic theory. The other half looks at economic growth over a longer period. In a pair of papers written in 1956 and 1957, Solow revolutionized growth theory. His work attempted to quantitatively decompose the sources of growth. Challenging the beliefs of many economists at the time, he concluded that changes in capital and labor were relatively unimportant. The remainder, which has since been called the “Solow Residual” was attributed to “total factor productivity” (TFP) and interpreted as changes in technology. Concurrent research by Moses Abramovitz confirmed Solow’s findings, giving TFP 90% of the credit for economic growth in the US from 1870 to 1950. In the RBC model, the size of technology shocks is found by subtracting the contributions of labor and capital from total output. What remains is TFP.

“A Measure of Our Ignorance”

Because TFP is nothing more than a residual, it’s a bit of a stretch to call it technical change. As Abramovitz put it, it really is just “a measure of our ignorance,” capturing the leftover effects in reality that have not been captured by the simple production function assumed. He sums up the problem in a later paper summarizing his research

Standard growth accounting is based on the notion that the several proximate sources of growth that it identifies operate independently of one another. The implication of this assumption is that the contributions attributable to each can be added up. And if the contribution of every substantial source other than technological progress has been estimated, whatever of growth is left over – that is, not accounted for by the sum of the measured sources – is the presumptive contribution of technological progress
Moses Abramovitz (1993) – The Search for the Sources of Growth: Areas of Ignorance, Old and New p. 220

In other words, only if we have correctly specified the production function to include all of the factors that determine total output can we define what is left as technological progress. So what is this comprehensive production function that is supposed to encompass all of these factors? Often, it is simply
Y=AK^\alpha L^{1-\alpha}

Y represents total output in the economy. All labor hours, regardless of the skill of the worker or the type of work done, are stuffed into L. Similarly, K covers all types of capital, treating diverse capital goods as a single homogeneous blob. Everything that doesn’t fit into either of these becomes part of A. This simple function, known as the Cobb-Douglas function, is used in various economic applications. Empirically, the Cobb-Douglas function matches some important features in the data, notably the constant shares of income accrued to both capital and labor. Unfortunately, it also appears to fit any data that has this feature, as Anwar Shaikh humorously points out by fitting it to fake economic data that is made to spell out the word HUMBUG. Shaikh concludes that the fit of the Cobb-Douglas function is a mathematical trick rather than a proper description of the fundamentals of production. Is it close enough to consider its residual an accurate measure of technical change? I have some doubts.

There are also more fundamental problems with aggregate production functions that will need to wait for a later post.

Does TFP Measure Technological Progress or Something Else?

The technical change interpretation of the Solow residual runs into serious trouble if there are other variables correlated with it that are not directly related to productivity, but that also affect output. Robert Hall tests three variables that possibly fit this criteria (military spending, oil prices, and the political party of the president), and finds that all three affect the residual, casting doubt on the technology interpretation.

Hall cites five possible reasons for the discrepancy between Solow’s interpretation and reality, but they are somewhat technical. If you are interested, take a look at the paper linked above. The main takeaway should be that the simple idealized production function is a bit (or a lot) too simple. It cuts out too many of the features of reality that are essential to the workings of a real economy.

TFP is Nothing More Than a Noisy Measure of GDP

The criticisms of the production function above are concerning, but subject to debate. We cannot say for sure whether the Cobb-Douglas, constant returns to scale formulation is close enough to reality to be useful. But there is a more powerful reason to doubt the TFP series. In my last post, I put up these graphs that appear to show a close relationship between the RBC model and the data.

Source: Harald Uhlig (2003): How well do we understand business cycles and growth? Examining the data with a real business cycle model.
Source: Harald Uhlig (2003): How well do we understand business cycles and growth? Examining the data with a real business cycle model.

Here’s another graph from the same paper

Source: Harald Uhlig (2003): How well do we understand business cycles and growth? Examining the data with a real business cycle model.
Source: Harald Uhlig (2003): How well do we understand business cycles and growth? Examining the data with a real business cycle model.

This one is not coming from a model at all. It simply plots TFP as measured as the residual described above against output. And yet the fit is still pretty good. In fact, looking at correlations with all of the variables shows that TFP alone “explains” the data about as well as the full model

Source: Harald Uhlig (2003): How well do we understand business cycles and growth? Examining the data with a real business cycle model. Second column shows the correlation from the full RBC model and the third with just the TFP series
Source: Harald Uhlig (2003): How well do we understand business cycles and growth? Examining the data with a real business cycle model. Second column shows the correlation from the full RBC model and the third with just the TFP series.

What’s going on here? Basically, the table above shows that the fit of the RBC model only works so well because TFP is already so close to the data. For all its talk of microfoundations and the importance of including the optimizing behavior of agents in a model, the simple RBC framework does little more than attempt to explain changes in GDP using a noisy measure of GDP itself.

Kevin Hoover and Kevin Salyer make this point in a revealing paper where they claim that TFP is nothing more than “colored noise.” To defend this claim, they construct a fake “Solow residual” by creating a false data series that shares similar statistical properties to the true data, but whose coefficients come from a random number generator rather than a production function. Constructed in this way, the new residual certainly does not have anything to do technology shocks, but feeding this false residual into the RBC model still provides an excellent fit to the data. Hoover and Salyer conclude

The relationship of actual output and model output cannot indicate that the model has captured a deep economic relationship; for there is no such relationship to capture. Rather, it shows that we are seeing a complicated version of a regression fallacy: output is regressed on a noisy version of itself, so it is no wonder that a significant relationship is found. That the model can establish such a relationship on simulated data demonstrates that it can do so with any data that are similar in the relevant dimensions. That it has done so for actual data hardly seems subject to further doubt.
Hoover and Salyer (1998) – Technology Shocks or Coloured Noise? Why real-business-cycle models cannot explain actual business cycles, p.316

Already the RBC framework appears to be on shaky ground, but I’m just getting started (my plan for this series seems to be constantly expanding – there’s even more wrong with macro than I originally thought). My next post will be a brief discussion of the filtering method used in many DSGE applications. I will follow that with an argument that the theoretical justification for using an aggregate production function (Cobb-Douglas or otherwise) is extremely weak. At some point I will also address rational expectations, the representative agent assumption, and why the newer DSGE models that attempt to fix some of the problems of the RBC model also fail.

 

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