Why Economists could do with Time Travel

Once upon a time there was a little theory that sought to be validated…


Theoretical foundations of the Consumption Correlation Puzzle

Standard economic theory is of the notion that with economies that are increasingly open in their international trade relations interacting in a globalised world, each economy should strive to smoothen its consumption across time. Naturally, it is expected that just as individual consumers partake in consumption smoothing over their expected lifetimes, so must economies at an aggregate replicate these tendencies.  The result ought to be a strong correlation arising out of the consumption pattern among countries and this correlation would be higher than that observed for output- the thing which fluctuates inherently and thus, presents the argument for consumption smoothing in the first place. The origin of the Backus-Kehoe-Kydland consumption correlation puzzle is the puzzling lack of empirical evidence that would corroborate these straightforward hypotheses, finding instead upon examination that consumption is, in fact, much less correlated across countries than output.

Time for some Recreation(al)activity

In order to replicate the exercise carried out in the original study by Backus, Kehoe and Kydland (1992), annual data for twelve countries (Australia, Austria, Canada, Finland, France, Germany, Italy, Japan, South Africa, Switzerland, the United Kingdom and the United States of America) was used, the very same that have been included here as well. This data was arrived at in the form of GDP for output and Households and NPISHs Final Consumption Expenditure (formerly Private Consumption Expenditure) for consumption in constant 2010 US$ (in order to deal with real rather than nominal figures) spread across the time period 1993, following up after the year of publishing of Backus et al. (1992), upto 2019, the latest year for which data was available in the World Development Indicators Dataset.

In line with the mathematical operations performed in Backus et al., detrended components (using the Hodrick-Prescott filter) of the natural logarithm of both variables was  taken for computing correlation coefficients across the twelve countries from 1993 to 2019, that is to say that any fluctuation (mostly business-cycle related phenomena) from the long-term trend was removed so that the short-term ups and downs did not cloud the real changes happening on the big stage aka in the longer run. This is reproduced below where the serial numbers 1-12 in the variable names correspond to the twelve aforementioned countries in alphabetical order:

Correlation of Output

Correlation of Consumption

As can be seen, these tables present a slightly different outcome than the one that emerged in the paper giving rise to the puzzle:

Source: Backus et al. (1992, p. 8)

The Facts

An emergence of stronger correlations is seen between the consumption and output figures of the countries and the United States in the last row of each table (with the exception of Italy where cross correlation of consumption is negative). Correlation coefficients computed here (barring Italy) are positive and higher in magnitude than their original counterparts; the originally negative values for France, Finland and South Africa have turned positive. Moreover, while the average correlation coefficient for the eleven countries with the US came out to be .1864 for consumption and .3064 for output in the analysis done by Backus et al., the values here were .5200 and .6328 respectively. If all cross-correlations are to be considered i.e. each possible pairing of one country with another, these averages being .3498 and .6290 are lower than the averages of those for cross-correlations with the US.

Changing times, changing tides?

These results, however, are testament to the idealistic scenarios provided by economic theory being realised to some extent (all is not lost after all), although slowly and with somewhat of a delay. Almost as early as mid-last century, economic theory suggested that with open economies and free flow of goods, services and capital in international markets, the consumption across countries ought to be more strongly correlated than output. In other words, economists thought of the world as being one grand potluck- the more (less) any one country brings to the table, the better (worse)-off everyone else is for it.

While economies around the world had been open for several decades at that point, not to mention trade ties that had existed since centuries, with many more joining their leagues in the ensuing years, there continued to be major barriers to the unfettered flow of goods and services across borders. Markets were riddled with imperfections in the form of tariffs and quota restrictions, besides special favours lent to countries with whom bilateral and/or regional trade agreements had been signed. Comparative advantage, though gaining ground, was being exploited nowhere near the level it is at present. As a result, something was predicted in theory, namely that risk sharing should have taken place to eliminate the contingency of any one country having to bear the brunt of a downturn in its economy leading to reduced production of output and hence, reduced consumption.

Except, all the while, something else entirely at odds with this paradigm was afoot. There was hardly any risk sharing taking place among countries which was what the BKK puzzle picked up on. Neither can this result be caused by having analysed a group of countries that were either closed or in the transition process from closed to open (as in the case of India in the 1980s and 1990s) for the authors consider a cohort of developed, industrialized nations that had been engaged in trade and economic transactions since some time. One reasonable argument that stands out and indeed, seems to explain a host of such ‘puzzles’ identified around the same time as this is the presence of a so-called ‘Home Bias’. This instilled prejudice in favour of home-sweet-home pervades individuals’ decisions of consumption and investment whereby these are disproportionately affected by the conditions of their own home country- a bias that can easily preclude diversification of risk and mitigation of consumption smoothing. Not only are all eggs being put in one basket, the basket is the same for the entire country. No wonder then that it never rains, but it pours.

Have we learnt from our mistakes? Well, it’s complicated.

The argument that can explain the results of correlation computed by us (which turn out to be more than twice as large on average), namely that of there being a highly interconnected economic ecosystem, at least of the countries studied, particularly in the financial sector, accounting for the increased coefficients of correlations. Since we see positive coefficients that were higher for all but one of the comparisons for both consumption and production, it may just so happen to be the case that the economic performance of these countries are highly interdependent on one another which is driving the correlation observed in output. Consumption in each country may very well be correlated with its output (courtesy of Home Bias) and this spills over in the correlation between country-specific consumption data. As it is, even now the correlation in output stands higher than in consumption. Looks like things haven’t changed all that much.

This is not to say that there is no scope for risk sharing in the present scenario either. Au contraire in fact, except that it is highly likely that the risk sharing is financial in nature. It is taking place in the form of mutually directed investments to and from the centre of study i.e. the United States and the other countries in the form of various financial and capital assets. Since these components of the financial market are sacrosanct in fostering economic growth, it goes without saying that they can easily disburse the effects of both positive and negative shocks to one nation’s economic system out to the rest of the participants in the market, involving them in the ensuing impact as well. A more recent example that comes to mind is the 2008 financial crisis.

Consequently, it may be surmised that the factor driving the high correlations in both cases is the interconnectedness of production and through that channel then, also consumption. Then again, the coefficients being in the moderate range can also be attributed to the fact that each country’s indicators for output and consumption are being compared to only one other country’s at a time. Furthermore, with globalisation there have emerged possibilities of establishing economic ties with countries all over the world and not just a select bunch that lie by and large in the same category of economic performance (measured by indicators of standard of living such as level of Per Capita Income). This leaves our collection of twelve in a precarious position in that it is far from capturing the bigger picture of international economic relations.

We’re all in this together

Economic theory seems to have predicted (somewhat naïvely) consumption smoothing taking place in the event that an economy experiences an unusually high or low production period that is only dependent on its own economic performance independent of that of other countries with whom it trades. Risk sharing would, ceteris paribus, allow the individuals in said economy to benefit from the avenues of trade with the objective of precluding any sudden, unforeseen outliers in their pattern of consumption by distributing the risk across the many partner economies. It is nothing else but the innocuous ceteris paribus assumption that hastily breaks down here (doesn’t it always?). Economic shocks are no longer viable to treatment as deus-ex-machina-like events that upend economic activity in well-demarcated patches of the Earth better known as countries in isolation from the rest of the world, instead they topple the entirety of an inextricably linked economic framework like a gust does a house of cards.

Is economic theory long-sighted or is the world short-sighted? Both, actually

Economic theory is often criticised for building on simplifying assumptions that make its models and predictions an apparent poor fit for the actual state of affairs. Then again, with time and technology many of these assumptions are coming true. It helps to think of reality as tending towards economic theory as certain barriers, say those in the way of complete markets, are steadily being broken down.

Consider the argument one of the authors (collaboratively) partook in setting forth the year following the birth of the BKK puzzle— trade imperfections due to non-traded goods (Backus & Smith, 1993). This also makes an appearance in one of the offered explanations of the correlation anomaly (Stockman & Tesar, 1995) and deserves lending some credibility to because it certainly makes for a compelling argument even now, decades after its conception. We are not yet in the day and age where, for instance, teleportation is an asset that providers of services can boast about, still strides have been made. Telemedicine, at least, has the potential of allowing you to avail health services from overseas.

Nevertheless, trade imperfections are not merely limited to the presence of non-traded goods; in fact, the very nature of exports and imports, no matter the advancement of shipping routes and global supply channels, is one of substantial trade costs which is in clear violation of the assumption of complete markets. At least until an ‘internet of things’ makes its way into existence, there are palpable difficulties in arbitrarily increasing or decreasing the volume of a country’s imports and/or exports. When this must be accomplished subject to ideal consumption smoothing in the event of either an adverse or favourable shock to its economic setup, the costs of disruption soon pile up in a short while. It is not clear if individuals would prefer sticking to the status quo (where exports and imports stand to tide over the short period of time where the anomaly in ecp\onomic performance arises), especially if they see this as a small price to pay in comparison to the added interventions required in recalibrating the forces of demand and supply in the domestic and foreign markets. That too assuming they even wish to smooth consumption at the cost of letting go of the aforementioned ‘Home bias’.

No, trade is not a zero-sum game

Another conclusion that can be drawn from the analysis at hand deals with Stockman and Tesar’s (1995) second argument, the one dealing with a sort of ‘crowding-out’ of foreign consumption by an exogenous increase in a country’s domestic demand. Although this effect is not revealed in the majority of the data— all of six cross-country correlation coefficients out of a total of hundred and thirty-two (which amounts to one in output and five in consumption out of sixty-six in each) come out to be negative. This does not go to say that it is absent in the remaining ones. It may be that the negative crowding-out effect is overpowered by the interconnectedness driving the positive correlations. At any rate, both the small magnitude of these negative coefficients and the relative strength of the oppositely-directed effects is enough to render it a secondary factor in the scheme of things.


I’ve got some good news: Economic theory isn’t just all wishful thinking. It’s a tad bit futuristic; maybe even slightly optimistic, sure, but not downright impossible. If there’s a theory in place, its proof ought not to be too far out there in the future. Besides, a subject can dream, right? All things come to those who wait. Just you see (or don’t, because as a certain someone opined, “In the long run we are all dead”). Lucky for him, of course, he’s far from it. For the rest of us, better get a move on, eh? That time machine won’t build itself.

-Anoosheh Zahra Mirkhushal

SY B.Sc. Economics


Backus, D. K., Kehoe, P. J., & Kydland, F. E. (1992). International real business cycles. Journal of political Economy, 100(4), 745-775.

Backus, D., Kehoe, P. J., & Kydland, F. E. (1993). International business cycles: theory and evidence (No. w4493). National Bureau of Economic Research.

Backus, D. K., & Smith, G. W. (1993). Consumption and real exchange rates in dynamic economies with non-traded goods. Journal of International Economics, 35(3-4), 297-316.

Stockman, A., & Tesar, L. (1995). Tastes and Technology in a Two-Country Model of the Business Cycle: Explaining International Comovements. The American Economic Review, 85(1), 168-185. Retrieved March 11, 2021, from http://www.jstor.org/stable/2118002

Obstfeld, M., & Rogoff, K. (2000). The six major puzzles in international macroeconomics: is there a common cause?. NBER macroeconomics annual, 15, 339-390.

Uhlig, H. F. H. V. S., & Ravn, M. (1997). On Adjusting the HP Filter for the Frequency of Observations. Tilburg University, School of Economics and Management.

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