How to estimate Italian parking data starting from German parking data?

I'm not entirely sure this would be possible to do using German data, though very happy to be corrected.

It seems that the data you have is largely driven by parking search costs, therefore could you not try and find internationally comparable data on travel to work time, control for a few bits and then try and see whether you can find parking search costs as having a significant effect? Then you could just apply that effect to the data on italian travel to work time and make the assumption that's reasonable.

For data: The Italian statistical authority (https://db.nomics.world/ISTAT) provide some brilliant survey data on citizens views on quality of life - perhaps there's something you could infer from there, or view whether data is offered on expenditure on parking enforecemnt. Similarly, the WEF's Travel and Tourism/Global competitiveness index may have indicators on travel to work time.

A very all out approach would be to collect data on council meeting minutes to see how often parking comes up as an issue.

If I had this problem and I wanted to estimate it for Italy, but could not get access to Italian data, then I would construct a Bayesian model and treat it as free parameters in one of two ways.

First, you could take the grand mean and the joint variance and construct a maximum entropy distribution for the mean and the variance jointly. You could then marginalize that out by noting that $$Pr(tilde{x}|mu;sigma^2)=int_{-infty}^inftyint_0^inftymathcal{L}(tilde{x}|mu;sigma^2)pi(mu;sigma^2)mathrm{d}mumathrm{d}sigma^2.$$

That would give you a crude distribution by assuming the data is representative. It would be overly wide if you used a maximum entropy distribution. That is called the prior predictive distribution. The two assumptions, both of which are dangerous, is that the data is representative and that there is nothing unique to Italy.

The second option is also Bayesian. The reason is that Bayesian methods allow you to incorporate related information into your estimates. It produces a stochastically dominate estimator by doing this but does require a bit of judgment and skill to do well.

The second is to estimate parking pain from independent variables in each of these countries. I do not know enough about the topic to give you any. However, you could regress the parameters over some set of data where you have access to the parameters in Italy.

Let us imagine that your estimates for the three countries are $(beta,Sigma)$ where $beta$ is the vector of slopes and $Sigma$ is the covariance matrix. We will assume normality unless there is a reason otherwise.

Bayesian estimates do not produce point parameters but entire distributions for each parameter. We would marginalize out these parameters and create a prediction for Italy from them.

If $y$ is parking pain in Italy and $x$ are the factors available in all four countries, then you could construct $$Pr(y|x)=int_betaint_Sigmamathcal{L}(y|beta,Sigma,x)pi(beta,Sigma)mathrm{d}betamathrm{d}Sigma.$$ If you wanted a single point prediction, then you would maximize a utility function or minimize a loss function over the prediction.

It will all depend on the granularity of your data sets.

If you have not used a Bayesian method before, I would recommend getting Boldstad's two books on it. One is written for an upper division undergraduate, the other clearly is not.

What makes a Bayesian method different is that it does not assume that the data is drawn by chance. The data was seen, there is nothing random about it. The parameters are considered random numbers where random is meant as having uncertainty about their location.