Showing posts with label Probit models. Show all posts
Showing posts with label Probit models. Show all posts

Thursday, 21 February 2019

Assessing recession probabilities

Over recent months I have spent far more time than is healthy looking at political issues and I will return to them again. But for a pleasant change I wanted to look at some economics, specifically some quantitative analysis of the outlook for the UK. Brexit considerations aside, the UK faces headwinds from the global economic cycle which has lost significant momentum in the last couple of months – indeed the slowdown has come upon us more quickly than imagined. Within Europe, Italy fulfils the technical definition of recession, having posted two consecutive negative quarters of GDP growth in the second half of last year whilst Germany has only just avoided the same fate, with a flat Q4 growth rate following a contraction in Q3 2018. Despite all the concerns regarding the gilets jaunes protests, France did not do badly with quarterly growth of +0.3% in each of Q3 and Q4. The UK did even better, with a +0.6% rate in Q3 followed by a more modest expansion rate of 0.2% in Q4.

But that is all in the past. What about the outlook for the remainder of 2019? Obviously Brexit remains the elephant in the room as far as the UK is concerned, so it is impossible to be precise about what is likely to happen. In terms of what the evidence tells us so far, we know that business fixed investment fell in each of the four quarters of 2018, and in the second half the pace was particularly rapid with spending down 2.6% in real terms in Q4 relative to Q2. By end-2018 the volume of activity was thus the lowest since Q3 2015, and the second lowest quarter in four years. It is possible that it will rebound in the absence of a no-deal Brexit but latest CBI survey evidence continues to suggest that companies are likely to cut capital investment over the next twelve months.

However, declining business investment is not necessarily a good indicator of what will happen to overall GDP. In 14 of the last 53 years business investment has actually fallen at the same time as GDP has expanded. For four consecutive years between 2001 and 2005, when GDP growth averaged 2.7% per annum, business investment declined at an average annual rate of 2.8%. It is thus illustrative to look at the information content in other data to see what it tells us. In doing so, I have relied on the literature on qualitative choice models which tries to find leading indicators to predict recession probabilities (see this New York Fed paper for insight into how such models have been applied in the context of the US).

In applying the analysis to the UK, the object of the exercise is to find indicators which have decent predictive power. I finally opted for the CBI’s business optimism index and the Conference Board’s leading indicator, which is in turn comprised of eight variables (order books, expected output, consumer confidence, bond prices, equity prices (All Shares), new orders, productivity and corporate profits). Although the leading indicator does contain financial variables, equities have a weight of less than 4% so I added a series for real equity prices (using the consumer spending deflator as the relevant price index) to specifically account for the fact that markets often spot downturns in the economic cycle more quickly than the published economic data.

As noted above this methodology uses models of qualitative choice. Such techniques are used to model outcomes where the dependent variable takes a binary 0,1 value depending on the contingent state. In this case the dependent variable is the year-on-year rate of real GDP growth which takes the value 1 when it falls into negative territory and 0 otherwise. Thus what the model tries to do is assess the likelihood that annual growth will turn negative [1]. Based on data back to 1973, we have 184 quarters of data, and on 25 occasions GDP growth turned negative. Using a basic probit model, I estimated a relationship between lagged values of the three explanatory variables and the binary dependent variable to give an assessment of recession probabilities six months ahead.
As the chart shows, on the four occasions since 1973 that growth has gone into negative territory, the model has predicted this six months ahead of time with an accuracy rate of at least 90%. The model suggests that on the basis of current data there is a probability of around 33% that GDP growth will turn negative by mid-2019. In order for that to happen by Q3 would require a sluggish Q1 growth rate and modest declines in Q2 and Q3 (i.e. a technical recession). Absent a Brexit-related collapse, this would appear to be a stretch. Thus the model likelihood of around one-third appears reasonable – an unlikely, but not impossible, scenario.

In contrast to conventional forecasting techniques, we do not attempt to quantify the rate of GDP growth. But the probabilistic approach outlined here gives a sense of the risks surrounding the outlook and thus some steer on how much preparation may be required to offset the worst-case outcomes. Obviously, the analysis is based on the information content in current data and is subject to changes resulting from random shocks. Brexit could thus significantly change the picture, but that is a subject for another day.


[1] Strictly speaking we ought to be looking at quarterly GDP growth to define those periods where there are two consecutive quarterly declines, but there is such a lot of noise in the quarterly data that the equations do not fit the data particularly well.