Mabel Frances Timlin (1891-1976)

I had the honor and pleasure of delivering the 30th Timlin lecture in economics at the University of Saskatchewan last Wednesday. My talk was on Secular Stagnation, a topic I think Timlin would have approved of. I enjoy giving public lectures. It's fun to connect economic theory to real world policy issues in a public forum. I think I often learn more from the interaction with the audience than they do. It was also an opportunity to learn more of Mabel Timlin and her remarkable story.

Mabel Frances Timlin was born in Wisconsin in 1891. It's not clear what motivated to move to Saskatoon in her youth. In 1921 she found employment as a secretary at the University of Saskatchewan. Evidently unimpressed with the papers she was typing for the economics faculty, she decided to study the subject in her spare time. She eventually completed her PhD at the University of Washington and become an assistant professor at the University of Saskatchewan in 1941, at the tender age of 50. 

Her PhD thesis Keynesian Economics was published in 1942. I had our library order a copy so that I might read it before my lecture. I have to say that I was thoroughly impressed with it. Her book did not consist of a simple regurgitation of Keynes (1936). Instead, it was a courageous attempt to distill some of his most important ideas and extend them using dynamic general equilibrium theory. According to David Laidler (in a personal correspondence):

I think her 1942 book was the very first "Keynesian" text and, among other things, included the first drawing of a demand for money-interest rate curve showing a liquidity trap. Modigliani cited her in 1943, but inadequately. [Correction: Modigliani "Liquidity preference and the theory of interest and money" Econometrica Jan 1944.]

She evidently transformed the Canadian macroeconomics profession in terms of its application of formal economic modeling. She became Canada's first female full professor of economics, the first woman to serve as president of the Canadian Political Science Association, the first woman outside the natural sciences elected a Fellow of the Royal Society of Canada, and one of the first ten women to serve on the executive committee of the American Economic Association. 

I include a piece below, sent to me by Robert Dimand, that provides a few more details of her career. I think it's quite an inspiring story.  

Timlin, Mabel Frances (1891-1976)

     The Keynesian economist Mabel Timlin was the first tenured woman among Canadian economists, first woman elected president of the Canadian Political Science Association (which then covered all social sciences, including economics), the first woman outside the natural sciences elected a Fellow of the Royal Society of Canada (1951), and one of the first ten women to serve on the executive committee of the American Economic Association (1958-60), despite becoming an assistant professor only in her fiftieth year, after a long career as an academic secretary. She was born in Forest Junction, Wisconsin, on 6 December 1891, and, after studying at the Milwaukee State Normal School, taught in Wisconsin and rural Saskatchewan. She became a secretary at the University of Saskatchewan in 1921, while studying for a BA there. At first Timlin intended to study economics there, but after seeing the Department of Economics and Political Science she decided (probably correctly) that she could learn more economics on her own. She took a BA with great distinction in English in 1929, and then directed the university’s correspondence courses in economics. Mabel Timlin became an instructor in economics at the University of Saskatchewan in 1935, after completing graduate course work in economics at the University of Washington during summers and a six-month leave. Her doctoral dissertation at the University of Washington, supervised by the much younger Raymond Mikesell, was accepted in 1940 and published as Keynesian Economics (1942). In 1941, Timlin became an assistant professor of economics at the University of Saskatchewan (associate professor 1946, full professor 1950) and a member of the executive committee of the Canadian Political Science Association (vice-president 1953-55, president 1959-60).

     Keynesian Economics did more than introduce Keynesian theory into Canadian academic life. Timlin offered one of the early general equilibrium interpretations of John Maynard Keynes’s General Theory, and was particularly noteworthy in treating it as a system of shifting equilibrium, presented with innovative diagrams on which she collaborated with the eminent geometer H. S. M. Coxeter. Timlin began work on Keynesian Economics in 1935, before Keynes published his General Theory: Benjamin Higgins had come to Saskatoon from the London School of Economics in 1935 for a one-year appointment, carrying a copy of the summary of Keynes’s Cambridge lectures that Robert Bryce had presented in Friedrich Hayek’s LSE seminar.

     Beyond her work on Keynes, Timlin also expounded international developments in welfare economics and general equilibrium analysis to a Canadian audience more used to historical and institutional economics than to formal theory (e.g. Timlin 1946). Timlin (1953) sharply criticized the Bank of Canada for failing to follow Keynesian countercyclical stabilization policies during the Korean War inflation. Much of her later work (e.g. Timlin 1951, 1958, 1960) concerned immigration policy, emphasizing the economic benefits of freer immigration.

     Mabel Timlin never married. Generations of former students were her extended family. She remained active as a scholar long after her official retirement in 1959, publishing a major report on the social sciences in Canada in 1968. She remained devoted to the University of Saskatchewan despite job offers from such institutions as the University of Toronto, and died in Saskatoon on 19 September 1976.

                                                                                                                 Robert W. Dimand

Selected works

1942. Keynesian Economics. Toronto: University of Toronto Press.

1946. General equilibrium analysis and public policy. Canadian Journal of Economics

   and Political Science 12, 483-495.

1947. John Maynard Keynes. Canadian Journal of Economics and Political Science 13,

   363-365.

1951. Does Canada Need More People? Toronto: Oxford University Press.

1953. Recent developments in Canadian monetary policy. American Economic Review:

   Papers and Proceedings 43, 42-53.

1955. Monetary stabilization policies and Keynesian theory. In K. R. Kurihara (Ed.),

   Post-Keynesian Economics, London: George Allen & Unwin, 59-88.

1958. Canadian immigration with special reference to the post-war period. In

   International Economic Association, International Migration, London: Macmillan.

1960. Presidential address: Canada’s immigration policy, 1896-1910. Canadian Journal

   of Economics and Political Science 26, 517-532.

1968. The social sciences in Canada: Retrospect and prospect. In M. F. Timlin and A.

   Faucher, The Social Sciences in Canada: Two Studies, Ottawa: Social Science Research

   Council of Canada, 25-136.

1977. Keynesian Economics, with biographical note by A. E. Safarian and introduction

   by L. Tarshis. Toronto: McClelland and Stewart, Carleton Library.

Bibliography

Ainley, M. G. 1999. Mabel F. Timlin, 1891-1976: A woman economist in the world of

   men. Atlantis: A Women’s Studies Journal 23, 28-38.

Spafford, S. 2000. No Ordinary Academics: Economics and Political Science at the

   University of Saskatchewan, 1910-1960. Toronto: University of Toronto Press.

Secular stagnation then and now

Secular stagnation refers to a prolonged and indefinite period of slow growth and high unemployment (or subnormal factor utilization). When was the last time this happened in the United States? Most people are likely to say the 1930s. In fact, it was the 1970s.

The 1970s were tumultuous years. There was the Vietnam war, oil supply shocks, and Watergate. The anchovies had disappeared off the coast of Peru. Clothing styles ranged from dreadful to appalling. Disco music was in. It was an awful time for those of us who lived through it.

The seventies are also known for a significant slowdown in measured productivity growth. (See Cullison 1989 for a useful review of issues related to measurement and interpretation). The most common measure of aggregate productivity is called Total Factor Productivity, or TFP for short (See Hulton 2000.)

Aside: What is TFP?  Let Y denote the value of what is produced in an economy over the course of a year. Let (K,L) denote measures of the capital and labor services used to produce Y. Let F(K,L) denote an "aggregator function" that specifies the manner in which capital and labor are combined to form output. Given an assumed F and measurements on (Y,K,L), the TFP is computed as the residual TFP = Y/F(K,L). That is, the TFP measures the value of output unaccounted for by K and L. (Alternatively, think of TFP as measuring the average product of a list of factor inputs aggregated in a particular way.)

The San Francisco Fed produces its own "utilization-adjusted TFP" series here. This is what  what their measure of TFP looks like since 1960.

The shaded episodes were constructed using my eyeball metric, but I think that most people are likely to identify similar regions. 

There is the matter of just how to interpret the productivity dynamic above. Personally, I find it hard to believe that productivity just grows in a straight line that the undulations we see above constitute measurement error. My own inclination is to interpret this pattern through a Schumpeterian lens (see here).  Productivity growth appears in the form of growth-regimes. A productivity slowdown occurs when the economy switches from a high-growth regime to a low-growth regime. The economic shock is most pronounced in the first few years following a growth slowdown. (Related to this, see Zeira 1997.) 

Economic theory suggests that the real rate of interest should (ceteris paribus) be low in a low-growth regime (and high in a high-growth regime). Let me compute a measure of the real rate of interest by taking the annual nominal yield on U.S. treasury debt and subtracting annual PCE inflation. Here is what the data looks like. 

Well, not a perfect fit (remember the ceteris paribus part) but close enough, I think, to be intriguing. In particular, note that both low-growth regimes identified above are associated with significantly negative real interest rates. The early 1980s look odd by this view but, of course, we know that this era was associated with another type of regime change. In particular, Fed policy moved from a high-inflation regime to a low-inflation regime, with this regime change occurring in 1980 under Fed chair Paul Volcker. 

Here is how the unemployment rate correlates with the real interest rate and growth regime.

Low-growth regimes beget low real interest rates and high unemployment rates. This seems consistent with Alvin Hansen's secular stagnation hypothesis (see my earlier post here). The pattern is evident in the most recent episode, as it is in the 1970s. Except nobody called it secular stagnation back then.  

The 1970s may not be viewed as an era of secular stagnation because nominal interest rates and inflation were rather elevated in that episode. Secular stagnation, with its Depression-era origin, is more naturally related with low nominal interest rates and low inflation.  But as the following diagram shows, secular stagnation can occur in high-inflation regimes as well as low-inflation regimes. 

The 1970s episode was called stagflation (an era of high inflation and high unemployment).

The two low-growth regimes above were different in an important way. When the economy transitions from a high to low-growth regime, the shock of regime change produces uncertainty. Investors will naturally move resources out of capital expenditure and into safer asset classes. Here is a critical question: What are the safe asset classes when a productivity slowdown occurs? The answer to this question seems to vary across episodes.

In the 1970s, the USD and UST securities were not among the set of safe assets. This was in large part due to the "unanchoring" of U.S. monetary policy following the breakdown of the Bretton Woods fixed exchange rate system. In August 1971, President Nixon announced that the USD would no longer be pegged to gold. More importantly than this, the public likely did not believe that monetary policy would keep inflation in check through other means (it took Volcker to convince the public of this several years later). The added fiscal pressures of the Vietnam war and the Great Society spending could not have helped this perception. As a result, the safe assets back then did not include government securities. Instead, investors flocked to assets outside the direct control of government, like gold and real estate.

In the most recent episode, real estate was most certainly not considered a safe asset. Investors began to walk away from real estate in 2006. They then ran way in 2008. Ironically, it was the USD and UST securities that proved to be among the most highly regarded assets this time around. This is no small part attributable to the fact that U.S. monetary and fiscal policies are presently perceived to be "anchored" (unsustainable paths for money and debt are viewed as temporary departures from a long-run stable anchor).

It's worth thinking about just how large the worldwide demand for U.S. money/debt must have grown since 2008. We can infer this enhanced demand from two observations. First, the supply of debt was increased substantially. Second, the price of that debt went up, not down (safe bond yields generally declined). What might have happened had the Fed/Treasury not intervened in the way they did?

To answer this latter question, we can look to the "hard money, tight fiscal" policy regimes in place when a low-growth regime hit the U.S. economy in 1929. In the early 1930s, short-term bond yields plummeted as today, and CPI inflation ran close to negative 10%.  The unexpected and dramatic deflation--produced by an elevated demand for money against a fixed money supply--almost surely exacerbated the depth of the contraction through well-known channels.

The lesson here is that responsible monetary and fiscal policy "anchors" a regime, rendering its money/debt a safe asset. But anchoring a policy regime does not require strict adherence to a fixed asset supply rule, like the gold standard, or year-over-year balanced budgets. A credible regime will permit the supply of safe assets to expand "elastically" when the demand for the product is enhanced. Doing so can help stabilize inflation around its expected value. Of course, it is important to let the elastic snap back should economic conditions dictate. The experience of the 1970s demonstrates what can happen when a policy regime becomes unanchored.

The optimal conduct of monetary and fiscal policy over the longer term when a productivity slowdown hits is much less clear. Alvin Hansen expressed skepticism that expansionary monetary and fiscal policy could do much of anything beyond the initial shock period. If anything, it might even do some harm if, for example, such policies led to a very large public debt. Instead, Hansen favored what today we would label "pro-growth policies." His conclusions stemmed from the fact that he viewed growth slowdowns as the byproduct of slowing innovation and population growth--phenomena that monetary and fiscal policies are ill-equipped to deal with.

The situation is slightly different today in that, unlike in Hansen's time, there is presently a huge worldwide demand for U.S. treasuries. This demand stems from three major sources. First, the UST is used widely in the shadow banking sector (in repo and credit derivatives markets) as collateral, a sector that has grown significantly since the 1980s. Second, many emerging market economies want to hold USTs as a safe store of value. And third, there has recently been an added regulatory demand for USTs stemming from financial reforms like Dodd-Frank and Basel III. Because of these factors, it is likely that the U.S. economy can sustain a much higher debt-to-GDP ratio than it has in past.

Much of what one might recommend in terms of optimal policy stems from what is assumed to drive productivity (and population growth). For economies operating below the technological frontier (e.g., EMEs), productivity slowdowns might be avoided, in principle at least, through some type of policy change.  However, the case is much less clear (to me) for economies operating near the technological frontier, where the Schumpetrian dynamic is more likely to govern the productivity dynamic. Some may point to the innovations produced during the second world war as example of how expansionary fiscal policy might enhance productivity growth. But surely, basic research and development can be better subsidized in a more targeted manner, without appealing to a massive and broad-based fiscal expenditure.

Alvin Hansen's Secular Stagnation Hypothesis

The phrase secular stagnation was first introduced by Alvin Hansen in a speech he prepared for the AEA meetings in 1938: Economic Progress and Declining Population Growth. If you haven't read the speech, I recommend that you do--it's an interesting and easy read. (Alternatively, Tim Taylor provides a concise and accurate summary here: Secular Stagnation: Back to Alvin Hansen.)

Let's think about what things must have looked like for Hansen in late 1938. Earlier in the decade, the United States suffered a major economic contraction. From 1929-1933, real GDP declined by over 25%. And despite a robust period of growth from 1933-1937, the economy slipped back into recession in 1938. 

1938 must have looked disappointing (to say the least) for those living at the time. After a decade of economic hardship (the unemployment rate remained elevated throughout the episode) and recovery, the economy's capacity to produce material wealth in 1938 was no greater than its capacity in 1928. Was this the end of growth?

What sort of growth did Hansen have in mind? Well, writing in 1938, one would probably have been most impressed with the rapid rate of economic expansion that occurred in the late 19th century (the new technologies introduced early in the 20th century would have impressed as well, of course). That was an era of rapid technological progress, high population growth rates, and the widespread development of new territory. Associated with these developments was a rapid growth in investment opportunities and capital spending. Everyone seemed to be working hard. And even if progress was at times interrupted by recession, these episodes were short-lived with rapid recovery. (Personally, I don't think things were quite as rosy as the narrative above suggests, but let's stick to the main story.)

So that's roughly the evidence. What about theory? Hansen notes that earlier economists were focused mainly on how economic growth (driven by technological change, population growth, etc.) affected material living standards (the level of real per capita income). Later economists began to notice that growth and economic stability might be related (the central tenant of modern real business cycle theory). But more recently, Hansen writes, "the role of economic progress in the maintenance of full employment of the productive resources has come under consideration." (It is notable that the economists he cites for initiating this line of inquiry includes Wicksell and not Keynes; see David Laidler).

The theory Hansen espouses seems to relate the level of employment (say, as measured by the employment-to-population ratio or the unemployment rate) to the rate of economic growth. The rate of economic growth is determined by technological progress and population growth. Both of these forces are secular in the sense they tend to operate over extended horizons (i.e., over decades and not from quarter-to-quarter or year-to-year). The effect of growth is to elevate the desire for capital expenditure. A larger population stimulates the construction of residential capital. New industries and technologies stimulate the demand for business fixed investment. Workers are needed to build the stuff. Ergo, a higher rate of growth over long periods of time begets a higher rate of resource utilization over the same period of time (higher average employment rate, lower average unemployment rate).

But the story above is incomplete. After all, what was just described is not inconsistent with (say) real-business-cycle (RBC) theory. The equilibrium level of employment in that class of models could vary with the parameter that describes the economy's long-term growth rate (whether employment is increasing or decreasing in the growth rate is likely to depend on, among other things, the relative strength of substitution and wealth effects). It is theoretically possible to generate secular stagnation in an RBC model, where a low-growth regime generates a low-employment regime. But in the RBC interpretation, low employment could be an efficient outcome, given a lower pace of economic growth. It seems clear that Hansen is suggesting that the low employment observed in a low-growth regime is inefficient. He writes:

For it is an indisputable fact that the prevailing economic system has never been able to reach reasonably full employment or the attainment of its currently realizable real income without making large investment expenditures. 

This is a bit of a mischievous statement in that it commingles an alleged fact with theory. (I don't want to make too much of this now, but consider my post here, in particular, the passage by Richard Rogerson related to this issue). Hansen does not get into theory very much at all, except to say:

I shall not attempt any summary statement of this analysis. Nor is this necessary; for I take it that it is accepted by all schools of current economic thought that full employment and the maximum current attainable income level cannot be reached in the modern free enterprise economy without a volume of investment expenditures adequate to fill the gap between consumption expenditures and that level of income which could be achieved were all the factors employed. 

So my best guess of what we might have here is a version of Friedman's "plucking model" (with full employment serving as a ceiling or capacity constraint) combined with some classical notion of the difficulty associated with matching the flow of national saving with the flow of national investment. This process evidently does not work well as it should unless the demand for investment is high--which, in turn, is not generally possible unless the economy (technology and/or population) is growing rapidly.

While the hypothesis seems similar to Keynes (1936) in that depressed investment is the proximate cause of persistently high unemployment, there is (I think) an important difference. Keynes emphasized the role of "animal spirits" in determining investment demand. Depressed expectations over the "prospective rate of profit on new investment" might become a self-fulfilling prophecy (see Farmer). Although I could be wrong, I don't ever recall Keynes suggesting that the cure for high unemployment was more rapid technological progress. I think of Keynes (1936) as an explanation for depressed levels, unrelated to growth phenomena.

Hansen, on the other hand, could be interpreted as holding the view that expectations are more firmly anchored on economic fundamentals ("...we are forced to regard the factors which underlie economic progress as the dominant determinants of investment and employment.") For this reason, Hansen seemed less enamored than Keynes on the use of expansionary fiscal policy to combat high unemployment. After all, if the fundamental problem is low growth, attempts to boost "aggregate demand" can at best confer only transitory benefits. Moreover, these benefits may over time be swamped by cost considerations, like a mounting public debt.

Insofar as Hansen (1939) provides policy advice, it sounds not so much like a pro-growth agenda as it does a set of anti-anti-growth recommendations. To paraphrase: "Population growth is fading. There are no new territories to settle and exploit. We can only hope for more technological advancement, so don't do anything to hamper this last great hope of ours. Except that it seems that we are: the growing power of trade unions, trade associations, and other monopolistic practices are restricting technological advance. This is a great folly."

Hansen's secular stagnation hypothesis was largely forgotten over time. I'm not entirely sure why this was the case, especially in light of the subsequent popularity of Keynesian theory. Maybe it had something to do with their respective policy recommendations. Active demand management sounds more appealing than dismantling trade unions, I suppose.

I sometimes hear people suggest that Hansen's hypothesis fell out of favor because it was proved wrong. Shortly after he wrote, the growth factors took off and the unemployment rate remained low on average. However, Hansen did not exactly offer a prognostication--his theory is better thought of (like any theory) as a conditional forecast.

While the settlement of new territory played a big role in the past, it was not likely to do so in the future (and in fact did not, as of 2016). And while medical technology played a big role in lowering mortality rates in the 19th and early 20th century, "no important further gains in this direction can possibly offset the prevailing low birth rate." To say that Hansen did not forecast the coming baby boom is correct only insofar as Hansen did not make any forecast--just a conditional statement that if the prevailing low birth rate was to persist into the future, then low population growth would contribute to depressed demand for capital formation. He was, of course, plainly concerned that the trend might continue, but that's not the same thing as asserting it would. His caution in making predictions is evident when he writes:

Of first-rate importance is the development of new industries. There is certainly no basis for the assumption that these are a thing of the past. But there is equally no basis for the assumption that we can take it for granted the rapid emergence of new industries rich in investment opportunities as the railroad, or more recently the automobile, together with all the related developments, including the construction of public roads to which it gave rise. 

So maybe the pace of technological advance will accelerate. Or maybe it won't. It's not something we can take for granted. Hansen seems concerned about the prospect for future growth. But he's not asserting, as Robert Gordon seems to, that our best days are necessarily behind us. He notes, quite properly in my view, the sporadic nature of growth:

Nor is there any basis, either in history or theory, for the assumption that the rise of new industries proceeds inevitably at a uniform pace. The growth of modern industry has not come in terms of millions of small increments of change giving rise to smooth and even development. Characteristically, it has come by gigantic leaps and bounds. 

He cites D. H. Roberston for this view, but it is also a recurring theme in Schumpeter's work (see my earlier post relating Schumpeterian growth to secular stagnation). 

So, where does this leave us? No, I don't think Hansen's theory was proved wrong by subsequent developments. That the conditioning factors turned out not to prevail should not be construed as a rejection of the theory. The theory should be evaluated on other grounds. 

The central proposition is that high growth (via technology and or population) is necessary to keep labor near "full employment" (the level of output near "potential.") In particular, high growth is necessary to stimulate the capital spending that will employ the labor input. I am curious to know what sort of empirical evidence one might bring to bear on this hypothesis. We have a lot more data at our disposal than Hansen. How should this data be organized? Should we estimate a Hamilton regime-switching model on growth rate regimes and correlate estimated growth regime against the average employment-to-population ratio? As well, there is the perennial question of how to identify theoretical objects like "full employment" or "potential GDP" in the data.

And even if we should find support for the hypothesis, there is the question of what sort of intervention, if any, might be desirable. On this issue, Hansen writes:

How far such a [stimulative] program, whether financed by taxation or borrowing, can be carried out without adversely affecting the system of free enterprise is a problem with which economists, I predict, will have to wrestle in the future far more intensely than in the past.  

 Well, he certainly got that prediction right!

The Great American Slump

Back in 2010, I asked whether the U.S. might be in for a prolonged economic slump, similar to what Canada experienced in the 1990s (The Great Canadian Slump). It looks like the answer should have been "yes."

I think this is an interesting comparison because the slump in Canada was not precipitated by a financial crisis. Moreover, there was no "zero lower bound" issue at the time. Unlike in the U.S. today, the yields on Canadian government debt were high, not low.

Let's take a look at some data. Consider first the employment-population ratio (population of adults), or EPOP for short.

In the early 1990s, employment in Canada dropped very sharply and dramatically. This decline was as severe as the decline in U.S. employment during the great recession. It took roughly a decade for the Canadian EPOP to attain its previous peak. In the Great White North, this episode is called the Great Canadian Slump.

The parallel between these two recovery dynamics, for two different countries, at two different times, is really quite remarkable. The following diagram normalizes the EPOP to 100 at its cyclical peak (1990Q1 for Canada and 2008Q1 for the U.S.) and then plots the recovery dynamic in each case.

We can repeat the same exercise for the labor-force participation rate (LFPR).

The declining U.S. labor force participation rate has been much talked about, of course. Some analysts believe that the decline is driven primarily by demographics. Canada's LFPR has also declined since 2008, but not nearly as dramatically as the U.S. To the extent that Canadian and American demographics are similar, the comparison above suggests a more prominent role for other factors (e.g., differences in national policies, cyclical conditions, etc.). In an earlier post comparing U.S. border states to Canada and the rest of the U.S., the evidence suggests that differences in national policies may be important:

Let me finish up here with one more comparison. Here I plot real per capita GDP against EPOP for Canada:

Back then people were talking about "jobless recoveries." As you can see from the diagram above, that's quite a jobless recovery. Here's what the corresponding data looks like for the United States today:

I don't hear too much talk about "jobless recovery" in relation to the U.S. today. The language has shifted to describing this recovery dynamic as "secular stagnation."

I'm still not entirely clear what people mean by term "secular stagnation." The phrase was originally coined by Hansen (1939). Hansen argued that rapid growth in technology and/or population was necessary to keep the economy at "full employment." The proposition sounds like a version of Okun's Law, except that the relationship posited seems to be between the level of employment (EPOP) as a function of the growth rate of the economy.

Hansen did not have much to say about interest rates, except to remark that they're mainly symptomatic and that economists tend to make too much of them. This view seems somewhat different from the one espoused by Larry Summers, who attaches greater significance to low interest rates--even suggesting that they're a defining characteristic of secular stagnation. Moreover, unlike Hansen, he seems to suggest at times that the direction of causality can be reversed; i.e., that a policy that increases the level EPOP can stimulate GDP growth (both in the short and long run, I presume). This latter proposition sounds a bit like Verdoorn's law. I'll have a bit more to say about all this in a future post.

Low interest rate policy and secular stagnation

Nick Rowe's post on upward-sloping IS curves motivates today's musings. I'm sorry, but what follows is a tad on the wonkish side. It's intended mainly to promote a conversation with Nick. (You can look in if you want, but I'm sure most of you have better things to do on Christmas Eve!).

Consider the Solow growth model. Output (the real GDP) is produced with capital (K) and labor (N) according to a neoclassical aggregate production function Y = F(K,N).

Define y = Y/N (output per worker) and k = K/N (capital-labor ratio). Define f(k) = F(K/N,1). Then y = f(k). That is, output per worker is an increasing function of capital per worker.

If capital and labor are exchanged on competitive markets, then factor prices are equated to their respective marginal products. Let (w,r) denote the real wage and the real rental rate, respectively. Let 0 < a < 1 denote capital's share of income. Then,

[1] w = (1 - a)f(k) and r = af(k)/k

That is, the real wage is an increasing function of the capital-labor ratio (since labor becomes relatively scarce). The real rental rate for capital services is a decreasing function of the capital-labor ratio (since capital becomes relatively abundant).

Now, consider an economy populated by two-period-lived overlapping generations. People enter the economy as youngsters, they become old, and then they exit the economy. The population of young people remains fixed at N over time t = 0,1,2,... The young are each endowed with one unit of labor, which they supply inelastically at the going wage. Hence, N represents labor supply. The young save all their income and consume only when they are old. Saving is used to finance investment, which adds to the future stock of productive capital. For simplicity, assume that capital depreciates fully after it is used in production. (None of the results below are sensitive to these simplifying assumptions).

Since a young person saves his entire wage, the capital stock (per worker) evolves over time as follows:

[2] k(t+1) = (1 - a)f(k(t)) for t = 0,1,2,... with k(0) > 0 given (as an initial condition).

The transition dynamics are such that k(t) converges monotonically to a steady-state satisfying k* = (1 - a)f(k*).

The real interest rate at date t in this model is equal to the future (t+1) marginal product of capital (which is proportional to the average product of capital), R(t) = af(k(t+1)) = af((1 -a)y(t) ) / ((1-a)y(t) ).

The IS curve in this model is defined as the locus of real interest rates and output consistent with goods-market-clearing. In the present context:

[3] R(t) = af( (1-a)y(t) )/( (1-a)y(t) ).

Equation [3] describes a conventional downward-sloping IS curve. A higher level of income (because of more abundant capital) increases desired saving, which puts downward pressure on the real interest rate. Conversely, an increase in the real interest rate reduces aggregate demand.

Now, let's consider one of Nick's experiments. Begin in a steady state. Nick considers an exogenous 10% increase in the capital stock. I'll do the opposite experiment and consider a 10% decline.

The capital-labor ratio is now lower. From [1], the effect is to lower the real wage and increase the rental rate. From its depressed level, the real wage increases monotonically back to its steady-state level. From its elevated level, the rental rate declines back to its steady-state level. The real interest rate, in turn, jumps up and then declines back to its steady-state level.

In a competitive economy, these price adjustments reflect the underlying fundamentals. The shock renders capital scarce. Less capital depresses the demand for labor, which is reflected in a lower real wage. Capital scarcity means the the return to rebuilding the capital stock is high. As saving flows into capital spending, the scarcity diminishes, and the real interest rate falls back to normal levels.

Next, to follow Nick's thought experiment in a slightly different way, suppose that a central bank tries to keep the real interest rate low in the face of the shock just described above. In fact, suppose that the central can manage to fix the real rental rate (hence the real interest rate) at its initial steady-state level forever.

If r(t) = r* forever, then by [1] the capital-labor ratio must remain fixed for all t > 1.

An implication of this policy is that the real wage will not fall. It's not that it cannot fall (it would fall if the real interest rate was permitted to rise). The real wage needs to fall, temporarily, to maintain full employment. But because it will not fall, then something else has to give. The level of employment must fall. Since k* = K/N is fixed and since K falls by 10%, it follows that N must fall by 10% as well. The central bank's refusal to permit the real interest rate to rise has led to an increase in unemployment (instead of a decrease in the real wage).

But things are even worse than they seem. While a shock that evaporates a part of the capital stock is eventually replenished when factor prices are market-determined, the same is not true when either the real interest rate or the real wage is fixed. In a post I wrote earlier (here), I considered a fixed real wage. But Nick's column made me realize that the same result holds if we fix the interest rate instead. A "low interest rate policy" in this case leads to "secular stagnation" (the level of output and employment is lower than it should be) as depicted in the following diagram:

One way to read this result is that it vindicates Bill Gross' idea that artificially low interest rate policy constitutes a form of "financial repression" inhibiting the U.S. recovery (I criticize his views here.)

How seriously to take this result? I'm not so sure. A lot depends on the nature of the shock that is imagined to have afflicted the economy. In the experiment considered above, I just wiped out a fraction of the economy's capital stock--like a hurricane, or nuclear bomb. A more generous interpretation is that the shock stands in for an event that evaporates a fraction of the value of existing capital (not necessarily its physical quantity). People do not become any more pessimistic in the model as a result of the shock, which is why the economy transitions back to its initial steady-state when the price-system is left unencumbered. A depressed economic outlook, on the other hand, would serve to reduce real interest rates, not increase them as in the experiment above--and that sort of scenario would provide more justification for low-interest policy.

Merry Christmas, everyone.

Schumpeterian growth and secular stagnation

What is secular stagnation? The "secular" part suggests something that's persistent--in the order of decades (as opposed to the 2-5 year frequency usually associated with a business "cycle."). The "stagnation" part suggests a measure of under-performance. But what measure? Are we talking about lower than average growth in employment and incomes? Or are we talking about depressed levels, instead of depressed growth rates? Are we talking about both? Getting this straight makes a difference in how we want to approach thinking about the phenomenon in question.

In what follows, I'll take the view that secular stagnation refers to prolonged episodes in which growth in real per capita income (GDP) is lower than its long-run average.

Most economists agree that long-run growth in material living standards (real per capita income or consumption) is the product of technological progress. Contemporary business cycle models (at least, those used for monetary policy) assume that technological progress occurs more or less in a straight line. This abstraction may be fine for some purposes, but I never much liked it myself. As a PhD student, I was influenced by Schumpeter's 1939 masterpiece Business Cycles.

Schumpeter (1939) emphasized that there is no God-given reason to expect growth to occur in a straight line. Research and development, and the process of learning in general, can be expected to generate innovations of random sizes and at random intervals. Moreover, any given innovation takes time to diffuse. Economy-wide productivity does not jump instantaneously with the arrival of the internet. I like this quote from his book:

 ‘‘Considerations of this type [the difficulty of coping with new with new things] entail the consequence that whenever a new production function has been set up successfully and the trade beholds the new thing done and its major problems solved, it becomes easier for other people to do the same thing and even improve upon it. In fact, they are driven to copying it if they can, and some people will do so forthwith. Hence, it follows w that innovations do not remain isolated events, and are not evenly distributed in time, but that on the contrary they tend to cluster, to come about in bunches, simply because first some, and then most, firms follow in the wake of successful innovation.’’ [p. 100]

It was this passage that led me to think of a model in which technological innovation drove growth but in a manner that was uneven because of diffusion lags. The notion that a new general purpose technology might spread like a contagion to generate the classic S-shaped diffusion pattern in GDP seemed like a very interesting hypothesis to investigate.

I was also influenced by Zvi Griliches' famous empirical investigation of the diffusion of hybrid corn in the United States:

In my paper (actually, the second chapter of my PhD thesis, published in 1998 with Glenn MacDonald) I saw this:

And so Glenn and I built a dynamic general equilibrium model where firms were motivated to innovate and imitate superior technologies. We estimated parameters so that the model reproduced the smooth but undulating path of GDP depicted in the figure above. I think I see these patterns in more recent TFP data as well (source):

According to this interpretation, episodes of secular stagnation are largely an inevitable byproduct of the process of technological development and growth. Accepting such an interpretation does not, in itself, have any implications for the desirability of policy interventions. But it does call into question the efficacy of certain types of interventions. In particular, do we really believe that more QE will spur future economic growth? Or should policy attention be directed elsewhere?

Now, one might object, as Larry Summers does here, that "If the dominant shock were slower productivity one might expect to see an increase in inflation." The type of reasoning that underpins this view is the simple Quantity Theory of Money equation: PY=VM. Ceteris paribus (holding MV fixed) a decrease in real income Y should induce an increase in the price level P. Maybe the 1970s provides the empirical basis for this view.

But there is no theoretical reason to believe that productivity slowdowns, or indeed, expected productivity slowdowns, should be inflationary. It's very easy to demonstrate, in fact, that "bad news" in the form of a slowdown in productivity leading to depressed expectations over the net return to capital spending can cause a "flight to safety" to government debt instruments (including money). The effect of such portfolio substitution is to depress bond yields and the price-level (see here and here for example).  But even apart from these effects, the behavior of inflation depends critically on the nature of monetary and fiscal policy.

The Neo-Fisherian Proposition

The Neo-Fisherian proposition is that a persistent policy-induced increase in short-term nominal interest rates will lead to higher inflation in the long-run. John Cochrane, one of the main proponents of this view (along with my colleague, Steve Williamson) discusses the idea here. Visually, the proposition asserts something like this:

Of course, the conventional view is that raising the policy interest rate will cause inflation to go down, not up. The idea that the opposite might be true is evidently something to be ridiculed.

Wonder why world is in a mess? Neo Fisherians: ”lowering rates causes inflation to slow down & raising rates causes inflation to speed up."

— Ann Pettifor (@AnnPettifor) December 15, 2015

I can't help but think that Pettifor's view on the proposition was formed without first trying to understand it's underlying logic (but I could be wrong). Also note that the proposition is not inconsistent a higher interest rate leading to lower inflation in the short-run.

Why do people generally feel uncomfortable with the Neo-Fisherian proposition? I think that fellow Canuck Grep Ip of the WSJ gets at one reason here where he writes:

Neo-Fisherism has theoretical elegance but lacks intuitive logic. At its heart, neo-Fisherism says there is, somewhere, a fixed real rate that drives what the public expects inflation to be. Yet few people–even those who know what real rates are–have a firm view of what they should be. Their expectations of inflation are more likely to depend on past inflation, central bank or private forecasts, and the state of the economy. These expectations of inflation will then drive the returns they expect on saving and investment, not vice-versa.

The uncomfortable part is that despite this apparent lack of intuition underlying the proposition, it appears consistent with recent experience:

However, in a recent column, David Beckworth questions whether the proposition is consistent with what is happening in Japan. This led me to ask him:

@dandolfa The one that says raising interest rates is necessary to raise inflation. This is being violated in Japan. pic.twitter.com/vrOiJV6uUh

— David Beckworth (@DavidBeckworth) December 15, 2015

Now, it might seem strange to some of you that I asked him which Neo-Fisherian theory he was referring to, but I did so because there seem to be two different strains. But before I get to that, it's worth emphasizing that the proposition does not state that raising interest rates is necessary to raise inflation. (I stated the proposition above, go read it again if you have to.)

The first strain of the theory seems to rely entirely on rational expectations and the Fisher equation (without any reference to central bank balance sheets or the conduct of fiscal policy). The way this thinking goes is that the Fisher equation is just a no-arbitrage-condition. (No-arbitrage-conditions are compelling economic restrictions because if they did not hold, traders could make infinite riskless profits.) If a central bank raises the nominal interest rate, then for a given real rate of interest, the expected inflation rate must rise (else traders will be making infinite profits). This seems to be the interpretation favored by Stephanie Schmitt-Grohe and Martin Uribe (see my discussion here).

Personally, I am not sold on this interpretation. I prefer the second strain of the theory, which is related more to the fiscal theory of the price-level (as the name suggests, the theory emphasizes the role of fiscal policy in helping to determine inflation).  According to this interpretation, the proposition that "a persistent policy-induced increase in short-term nominal interest rates will lead to higher inflation in the long-run" must be qualified with the condition that the fiscal authority passively accommodate the monetary authority's policy decision (see my column here: A Dirty Little Secret.)

Intuitively, think of the following thought experiment. The Fed raises its policy rate and its widely expected to remain at this elevated level for the foreseeable future. The effect of this policy is to increase the carrying cost of debt for the government. Assume that the government services this higher debt burden not by cutting expenditures or increasing taxes, but by increasing the rate of growth of its nominal debt. Essentially, the government is printing "money" to finance interest payments on its debt. Then (assuming a constant long-run money-to-debt ratio) the money supply must start growing at this higher rate. Suppose that people generally understand this (a big supposition, I know). Then, people should revise their inflation expectations upward (and actual inflation should result, not because of inflation expectations, but because the monetary and fiscal authorities are printing nominal liabilities at a more rapid pace to finance the higher interest cost).

I'm pretty sure that David and others understand the proposition when it is framed in this manner. Whether this is what actually transpires is, of course, anybody's guess (consider this case study for Brazil 1975-1985). It's really  hard to forecast precisely how the fiscal authority (Congress) might react to higher interest rates. I do find it interesting, however, that fellow Twitterer Matt Yglesias noticed the following:

Impressive how quickly congress has stopped caring about the deficit even as the end of ZIRP means it actually might make sense to care.

— Matthew Yglesias (@mattyglesias) December 16, 2015

Impressive indeed. But if interest rates on U.S. treasury debt continue to rise, the debt-service problem will make the headlines soon enough. The debate will then turn to whether the U.S. should cut G and increase T (austerity) or permit more rapid debt expansion (and inflation).