Financial Development and Sectoral Output Growth in 19th Century Germany

3 Investment, credit and output growth - a VAR analysis

in the total forecast error variance. For this purpose, we conduct a variance decomposition
as a next step. Table 3 shows the variance decomposition for a forecast horizon of 5 and 10
years. We find that bank lending explains up to 24% of the forecast error variance of net
domestic product and up to 30% of the forecast error variance of investment. Although this
implies that other shocks seem to be more important, this is a relatively high number in a
VAR analysis.¹³

Cholesky Decompositions

In this section, we estimate the alternative approach of a Cholesky decomposition see
Tornell and Westermann (2005). Panel A and Panel B of figure 3 show the results of the
impulse response functions, generated from two different VAR’s. In this first VAR, we only
include net domestic product (NDP) and bank lending, in the second one, we include NDP
and investment. Panel A shows that there is a positive and significant reaction of net domestic
product to an unexpected shock in bank lending. Furthermore, in Panel B, we see that there
is also a significant reaction of investment to bank lending.¹⁴ The variance decompositions,
reported in table 4, show that the shock in bank lending explain 21% and 25% of the forecast
error variance. Thus, the results seem to confirm the finding from the previous section that
used generalized impulse response functions.

¹³ The estimation of generalized impulse response functions is a useful approach, as it allows for a representation
that needs very few assumptions about the underlying causal structure of the variables. This can be seen
in the graphs for instance by the fact, that none of the impulse response functions start from zero (due to
the assumptions on the recursiveness of the variables). As discussed above, a short-coming of this approach
is the lack of precise identification, when the contemporaneous correlation is fairly high.

¹⁴Note that these impulse response functions come from separate regressions. In a Cholesky decomposition it
is not feasible to include the three variables at the same time, as it does not exists a plausible ordering for
net domestic product and investment.

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