Econometric Modelling of the Aggregate Time Series Relationship Between Consumers Expenditure and Income in the UK

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Simple time‐series representations dominated quarterly permanent‐income/life‐cycle models of consumption in fit and predictive accuracy. However, an ‘error‐correction’model (ECM, using the log consumption/income ratio) reconciled both the theories and the evidence, and treated as the DGP, explained the connection between the time‐series and econometric equations.

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Institution: University of Exeter

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Simple time‐series representations dominated quarterly permanent‐income/life‐cycle models of consumption in fit and predictive accuracy. However, an ‘error‐correction’ model (ECM, using the log consumption/income ratio) reconciled both the theories and the evidence, and treated as the DGP, explained the connection between the time‐series and econometric equations.

Image courtesy of interviewee. December 4, 2023

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The speaker reflects on a paper they wrote 40 years ago while still a student, which is associated with their master's thesis. The paper gained notoriety for addressing non-stationary time series modeling, revealing a correct approach that gained attention in the research community—building upon prior, less recognized work. The paper primarily focused on modeling economic relationships between consumption, income, and other variables.

A key contribution was the concept of cointegration, originally popularized by Clive Granger, which allows non-stationary variables to be analyzed by transforming them into stationary combinations. The speaker's study compared various methodologies and highlighted discrepancies in results among different research approaches, particularly emphasizing the importance of using both levels and differences of non-stationary variables in modeling.

The paper suggested using growth rates and included economic theory, particularly the savings ratio, in its regression analysis. While initially seen as ad hoc, the approach ultimately showed robust predictive power over the years, maintaining relevance even as new data emerged.

The speaker notes that while their original understanding was limited, subsequent developments in macroeconomic research significantly expanded the framework of cointegration, leading to its acceptance as a crucial tool for analyzing economic data.

In summary, the discussion emphasizes the evolution of thinking about time series data in economics, the enduring impact of the speaker's research, and the broader implications for macroeconomic modeling techniques in light of the rational expectations revolution.

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X-TIMESTAMP-MAP:LOCAL=00:00:00.000,MPEGTS=900000

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This paper was written 40 years ago, Joll early

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when I was still a student.

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At least in part not the work was done as part

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of my master's thesis, actually, or part of the work,

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although, it didn't come out in 1978.

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I graduated in 1975.

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So I've had a bit of fun rereading this

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after many, many years at your suggestion

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and thinking, what did we do there?

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And, of course, it is a bit notorious as this,

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this paper, and I can tell you why it's notorious,

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I think in, in a few words.

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Um, it's the, it, it really did for the first time,

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not quite the first time,

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because my other teacher, Dennis Saga, because my co-author

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and mentor was David Hendry with this paper at,

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this is at the London School of Economics.

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Dennis Sagan had something similar in the paper 10 years

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previously, but nobody really noticed it.

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It was asked that caught the attention of the,

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the research community.

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And this was to discover the correct way

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of modeling non stationary time series,

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because it had been done in the wrong way for,

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you know, quite a while.

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And one of the things that our paper does is

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to look at various examples of consumption, income

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regressions,

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with various dynamic aspects built into them.

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Of course, the, the person whose name one should mention,

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because he's, he is the one that got the Nobel Prize.

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He's Clive Granger because he, invented

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and popularized the notion of cointegration.

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And basically that's what we were doing.

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We were doing cointegration, but we didn't know it.

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All we knew was that we found an equation which,

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contained rates of change of the, in other words,

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the differences from year to year of our variables,

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consumption and income and inflation, and the price level

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and things of that kind as well as the levels.

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Of course, the levels are trending.

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The levels are aren't staying in one place.

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They're not, they're non stationary.

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But what five grains of notice was

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that if you look at linear combinations

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of non-stationary variables,

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the result can be a stationary process and

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therefore can be put into the same equation.

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Now, an something which I'd rather forgotten about,

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but it's a very important aspect of the paper, is

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that it compares different studies which

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are looking at the same, same times zero.

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It is the same problem with the same sort of economic theory

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in their minds,

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and yet really getting rather different results.

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And the particular paper, which was a, a curiosity to us,

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was, I forget the title

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and the names of the authors wall was one of them

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because that's how he is identified in, in, in,

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in our paper as wall.

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At wall at al.

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These people had been reading a, an important book

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by two chaps called Boxing Jenkins, who were not economists.

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They were concerned with modeling,

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statistical modeling of time series for purposes such

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as forecasting and,

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and, what they were ba their, their, their philosophy,

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which was really important as merging about the same sort

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of time, was that you could only really construct

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relationships between variables when they're all stationary.

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In other words, when they, when they have a a,

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a fixed distribution, they don't wander off in the same way

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that, things like stock prices

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and, GDP, you know, these things grow over time.

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Well, that doesn't do, you can't build,

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although that's what of course, economists were attempting

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to do and still do, attempt to do, you know, at times.

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But that we need to model stationary time series.

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And if they're not stationary, when we,

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when we receive the data,

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well then we don't look at the level,

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we look at the change from period to period,

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because that will usually appear stationary.

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And so, you know, the, the, these,

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these researchers were following, this,

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this line in which they were looking at the differences,

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the growth rates of consumption

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and the growth rate of income,

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and showing indeed that they were closely related.

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But of course, their relationship can't really tell you very

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much about what's going on in the heads of consumers

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because the levels have been taken out.

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They have difference. So they're following a statistical,

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optimality, path,

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and yet they're throwing away any contribution

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of economic theory.

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The puzzle was that their, their model seemed

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to fit the data better than all the models,

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which incorporated economic theory by,

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by having good savings ratios

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and, relationship between consumption

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and income, as, part of them.

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So what, where did that leave us?

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Where it left us was that we thought we've gotta

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basically stick to this important notion

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that we can only really model stationary variables using,

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using regression techniques.

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Okay? Um,

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but on the same time, we want to get the levels

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of the variables as well as the differences

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of the variables into the equation.

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How did we do that? And in fact, the truth is that this was,

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I recall when I did this in my master's thesis,

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I was very apologetic.

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I said, this is totally ad hoc and stupid,

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but look, if I put the difference,

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and this is in logarithms,

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so it's really the log of a ratio.

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If I, if I put the difference of the logs

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of these two variables, well, with a, you know, last year,

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you know, we put a lag on so that, so that we have the,

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you know, the, the direction of causation appropriate.

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Uh, then the difference looks stationary

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and the changes are stationary.

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So the whole equation fits the box

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and Jenkins, prescription

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of best fitting stationary data.

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Um, and

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yet we've included the savings ratio in the equation, which

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therefore we expect to have some predictive power.

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Um, if, if it, it's, if, if, you know, the way

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that consumers behave informs how these data came to be.

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Um, and so I think that's what the, you know, what is known

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as the daisy paper, 'cause it's DHS

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and Y, the authors, of whom I'm the D

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and H is David Henry.

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Um, the other guys were only involved in the revision

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to do some extra data, you know, some extra,

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data analysis.

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So, I think we have to say the, the first version

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of this paper was just Davidson and Henry.

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So that's, that's how it all came, came about.

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Um, but what we were basically doing was saying, okay,

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you know, we, we've, we've, we've resolved,

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we've explained the difference

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between these different studies by saying,

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got on the one hand, follow the, you know, the,

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the box of Jenkins prescription.

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On the other hand, get the theory in there

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by getting the levels and

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the relationship between the levels.

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But reading that paper, in retrospect, of course,

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we had no idea really what we were doing,

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because Clive Granger hadn't yet read it.

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And the con, you know, the relevant concepts

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didn't, didn't yet exist.

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And this was, what amazingly grew over

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the next 20 years

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or so of macroeconomics research,

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which was the whole, the whole notion of cointegration

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that you, you, you look at collections

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of non-stationary variables.

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You don't ask if they're correlated

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because that's a notion which is only really

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relevant to stationary data.

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You ask if they're cointegration, which means

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that they have common trends.

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If you take suitable linear combinations of them,

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you get a stationary series, which can then be correlated,

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which is not co correlated with the growth with the,

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with the variables measuring differences

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from period to period.

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Um, now our equation

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did roll well because it turned out that,

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it fitted the data pretty well, but it was quite stable.

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I, I, I, there were subsequent studies oath

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for at least the next 15 years, which really found,

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you know, in other words, with new data that hadn't been,

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hadn't occurred when we wrote the original play.

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But going up into the 1980s,

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and it still fitted pretty well.

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It broke down eventually.

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I forget exactly when, sometime in the nineties

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that it collapsed.

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Um, but, so what this was telling us

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that we were isolating some,

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regularities in the data, that it wasn't the kind

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of regression which breaks down as soon

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as you add a new observation

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that hadn't been used to fit it.

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And of course, this is the, this is the problem

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with many regressions is that they, you know,

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they fit the sample well enough

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because you fix them to do so, put in one variable

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or another, but as soon as you bring in some new data,

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then you know, the whole thing falls apart.

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Well, the daisy consumption function

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really did rather well in that respect.

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Um, and, and it was u it was widely used, for,

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you know, by forecasters something, something similar.

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The, the whole ever correction idea.

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'cause the, where the ever correction,

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terminology comes from is precisely

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that you've got the savings ratio as it lags, as one

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of the explanatory variables.

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So if this moves, if people find that the

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saving more than they,

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than they do normally do in the long term,

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because their incomes have hopefully risen

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and their consumption has remained according

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to their usual habits and,

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and, so, golly, look, we've,

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we've got all this cash, let's go out

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and spend it on something.

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But this is something that doesn't happen immediately.

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It happens with an, with some irregular lag.

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So, so hence the error correction is that we assume

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that people focus on, of course, this doesn't only apply

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to consumption, it applies to lots of things, you know,

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money stock and, and, and, and,

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likewise in financial data, of course, there's also

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an awful lot of research has been done over the 40 years

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following, our original contribution

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in which, you know, this, this phenomenon

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of cointegration has turned up in a lot of places.

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And so it's been regarded as, as,

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as quite an important contribution to

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macroeconomic research, a great deal of the effort

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that took place in the latter half of the 20th century,

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you could say, into, into macroeconomic modeling,

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rather collapsed because it was pointed out that,

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that expectations, had to be modeled in terms

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of a complete,

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macroeconomic system rather than, you know,

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being simple, simple projections and,

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and essentially that, that, that, that large

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macroeconomic models, weren't expected

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to work very well, which we didn't anticipate, I think,

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at the time that we wrote this paper.

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So, so, so what, what is known as the rational expectations

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Revolution, rather shot a hole in some of this work.

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But, I think

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nonetheless, cointegration has continued to be a,

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you know, an, you know, an important tool in the Armory

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for understanding, non-stationary variables.

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