In a recent article in the British Journal of Political Science, Hübscher, Sattler, and Wagner (2023) investigate the effects of austerity on party system polarization. They regress election-on-election changes in polarization on a measure of fiscal consolidation and find that an average fiscal consolidation package increases polarization by 0.036 units, or around 0.1 standard deviations. The size of this effect does not change when the authors include a range of additional controls and country and period fixed effects. As is standard, the authors measure party system polarization as the share-weighted standard deviation of party positions,

\[ \varsigma_{V} = \sqrt{\sum_i^{N} v_i \cdot \left(\theta_i - \bar{\theta}\right)^2} \]

where \(v\) and \(\theta\) represent vote shares and party positions respectively, and where \(\bar{\theta}\) gives the vote-share weighted system mean. The authors take their measures of vote share and party position from Döring, Huber, and Manow (2022) for parliamentary systems.

Although Döring, Huber, and Manow (2022) provide excellent coverage of party positions, this coverage is not perfect, and the measure is somewhat idiosyncratic. The measure is an average of measures taken at different points in time. For some parties, the measure might be based on left-right scales from Castles and Mair (1982). For other parties, the measures might be based on more recent expert surveys. Additionally, even with the unstinting efforts of the ParlGov team to provide left-right measures for all parties, some party positions are missing. The number of missing positions is small ( 31), and the average vote share of parties with missing positions is small ( 3.5%). Perhaps for these reasons, the authors ignore missing observations when they calculate polarization.

Country | Year | Month | Vote share | Party |
---|---|---|---|---|

Italy | 2013 | 2 | 25.555 | Five Star Movement |

France | 2012 | 6 | 6.909 | Left Front |

Ireland | 2016 | 2 | 4.212 | Independent Alliance |

Italy | 2013 | 2 | 3.204 | Left Ecology Freedom |

Italy | 2013 | 2 | 2.250 | Civil Revolution |

Germany | 2013 | 9 | 2.200 | Pirates |

Italy | 2001 | 5 | 2.170 | The Girasole (‘Sunflower’) |

Portugal | 1991 | 10 | 1.706 | National Solidarity Party |

Spain | 2015 | 12 | 0.869 | Basque Country Unite |

Spain | 2016 | 6 | 0.768 | Basque Country Unite |

Table 1 gives some impression of this pattern by listing the ten largest parties for which Hübscher, Sattler, and Wagner (2023) lack a left-right position. The list includes a number of parties on the far-left (Left Ecology Freedom, Left Front, Civil Revolution).

The standard way of dealing with missing data is to use multiple imputation. It might seem a bit strange to use multiple imputation here. Normally, we take a data-set, multiply impute data-sets with missing values filled in, and run analyses on the multiply-imputed data-sets, and combine those results. Here, we multiply impute, *perform a summarizing operation on the data-set*, and then run analyses on summaries of those data-sets. That is, we impute party positions only in order that we can calculate their weighted standard deviation (=polarization).

One way to improve multiple imputation is to bring in auxiliary variables – variables which might not feature in the analysis, but which are correlated with the missing values we’re trying to predict. Here, I brought in a bunch of other measures from Chapel-Hill, V-Party, the Manifesto Project, and WikiTags. I interpolated data from Chapel-Hill by carrying the last value forward, but the data from V-Party and the Manifesto Project is specific to each election year. These three measures therefore vary over time. The WikiTags measure doesn’t vary over time, but has much broader coverage.

Here’s what the model looks like with and without multiple imputation. I’ve kept everything about the original model the same, even those parts I disagree with, like regressing on the difference between polarization in two successive years, or a change score.

Original | MI | |
---|---|---|

Constant | 0.003 | 0.003 |

[−0.023, 0.028] | [−0.023, 0.029] | |

Fiscal consolidation | 0.019 | 0.019 |

[0.009, 0.030] | [0.008, 0.029] | |

Num.Obs. | 166 | 166 |

R2 | 0.074 | 0.068 |

Num.Imp. | 20 |

It looks from Table 2 like multiple imputation hasn’t affected the analysis at all – the coefficient value is unchanged, and if anything the confidence interval is slightly narrower than it was before. The coefficient value gives the change in polarization associated with a fiscal consolidation capable of reducing the deficit by one percentage point of GDP. Given that the average (median) fiscal consolidation package is worth 1.9 percentage points, the effect of an average fiscal consolidation on polarization is 0.036 units. Given the standard deviation of polarization in the original data is 0.39 units, that’s a standardized effect size of around 0.1 comparing “austerity” to “no austerity” countries. That kind of effect size would ordinarily be regarded as “small”.

The great thing about multiple imputation, however, is that it allows us to use other measures which are more affected by missingness. I decided to re-estimate the model using those other variables. Let’s see what happens.

Original | V-Party | Chapel-Hill | MARPOR | Wiki | |
---|---|---|---|---|---|

Constant | 0.003 | −0.017 | 0.008 | −0.006 | 0.003 |

[−0.023, 0.028] | [−0.059, 0.024] | [−0.067, 0.082] | [−0.064, 0.052] | [−0.011, 0.017] | |

Fiscal consolidation | 0.019 | 0.014 | 0.013 | 0.009 | 0.005 |

[0.009, 0.030] | [−0.004, 0.032] | [−0.021, 0.046] | [−0.015, 0.033] | [−0.001, 0.011] | |

Num.Obs. | 166 | 166 | 166 | 166 | 166 |

R2 | 0.074 | 0.018 | 0.005 | 0.003 | 0.020 |

Num.Imp. | 20 | 20 | 20 | 20 |

As Table 3 shows, when we use any of these other measures, the effect of fiscal consolidation is smaller than what it was before. In the V-Party data – the left-right measure I trust the *most* – the effect is three-quarters of what it was before. In the MARPOR data – the left-right measure I trust the *least* – the effect is half what it was before. What’s more, in all of the other models, the 95% confidence interval on the effect runs below zero, and so the finding doesn’t reach conventional levels of statistical significance.

It’s for this reason that I think that the effect of austerity on polarization depends on the measure of party position that you use. I think it’s hard to argue that the ParlGov measure – a time-invariant aggregate of many different sources over different periods – is preferable to any of the measures here. I’d therefore go further, and say that whilst the effect of austerity on polarization is *very likely* positive, there is room for doubt about this, and the magnitude of the effect may be smaller than we first thought.

## References

*British Journal of Political Science*.