0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
20.0
22.5
25.0
0.025
0.050
0.075
0.100
0.125
0.150
0.175
Density of U
τ
q
U
(
τ)
% Unemployment
Figure 3: Distribution of OECD Unemployment 1960-1999. Souce: OECD.
One simple hypothesis we may have is that the lack of robust results in the existing literature on
the impact of institutions on unemployment is derived from the fact that different institutions come
into play with different force at different levels of unemployment, but their effects are confounded
at the mean. Thus, by looking at individual quantiles we may hope to discover effects that have
previously been obfuscated. Additionally, the use of quantile regression may provide a more robust
framework of estimation for this rather problematic data than the usual maximum likelihood setup
based on the normality assumption. Figure 3 shows the distribution of unemployment across OECD
countries across time to be bimodal with a long right tail and clearly censored at zero, thus assuming
gaussianity may lead to misspecification. from the very outset.
Before proceeding with the main estimation results however, let us quickly review the basic
quantile estimation set-up using Figure 3. The τ -quantile is the value q
U
(τ ), such that Pr[U ≤
q
U
(τ )] = τ , or F
U
(q
U
(τ )) = τ , where F
U
() is the the cdf of unemployment. This corresponds to the
area under the red curve bounded by zero to the left and by the vertical line at q
U
(τ ) to the right.
Now define
ρ
τ
(z) = (τ 1{z > 0} + (1 − τ)1{z ≤ 0}) | z |,
(1)
and denote the set of institutional covariates of country i at time t by X
it
.
19
Convention