  We compute the limit of the moments of the partition function
$Z_{N}^{\beta_N} $ of the directed polymer in dimension $d=2$ in the
subcritical regime, i.e. when the inverse temperature is scaled as $\beta_N
\sim \hat{\beta} \sqrt{\tfrac{\pi}{\log N}}$ for $\hat{\beta} \in (0,1)$. In
particular, we establish that for every $h \in \mathbb{R}$, $\lim_{N \to \infty
}
\mathbb{E}\big[\big(Z_{N}^{\beta_N}\big)^h\big]=\big(\frac{1}{1-\hat{\beta}^2}\big)^{\frac{h(h-1)}{2}}.$
We also identify the limit of the moments of the averaged field
$\tfrac{\sqrt{\log N}}{N} \sum_{x \in \mathbb{Z}^2}
\varphi(\tfrac{x}{\sqrt{N}})\big(Z_{N}^{\beta_N}(x)-1 \big )$, for $\varphi \in
C_c(\mathbb{R}^2)$, as those of a gaussian free field. As a byproduct, we
identify the limiting probability distribution of the total pairwise collisions
between $h$ independent, two dimensional random walks starting at the origin.
In particular, we derive that $$ \frac{\pi}{\log N}\sum_{1 \leq i<j\leq h}
\mathsf{L}_N^{(i,j)}\xrightarrow[N \to \infty ]{(d)} \Gamma\big(
\tfrac{h(h-1)}{2},1\big) \, ,$$ where ${\mathsf{L}}^{(i,j)}_N$ denotes the
collision local time by time $N$ between copies $i,j$ and $\Gamma$ denotes the
Gamma distribution. This generalises a classical result of Erd\"{o}s-Taylor.
