Can econometrics test for correlation or causality between prices and corruption? This week there was news that some prices are rising. I heard that in some countries where corruption is high the prices are also higher. I wonder if there is causaility or just both at same. It would be interesting to find some material to support if the claim is true. Is there some study e.g. comparing prices levels for energy and testing whether corruption levels in an economy (bribing, black market, unregulated markets) influences prices?
Some related studies:

Al-Marhubi, F. A. (2000). Corruption and inflation. Economics Letters, 66(2), 199-202.
The analysis is based on cross-country data consisting of 41 countries from Asia and Latin America for which data is available on four alternative indices of corruption (two from Transparency International, one is the Business International index, and the fourth from another economics study). Note that numerically, these are essentially non-corruption indicators -they range from $0=$ maximum corruption to $10=$  no corruption. The panel covers the period 1980-1995. Four alternative OLS regressions were run (each with one corruption indicator present), with heteroskedasticity-robust standard errors. In all cases a statistically significant positive correlation between corruption and inflation was found.  

How large a correlation (to judge its economic significance also)?  The dependent variable was the logarithm of inflation. The value of the coefficient on the corruption variable was on average $-0.22$. Given how the indicators are defined, the minus sign says that  less corruption = less inflation. The actual value roughly says that $1/5$ of inflation was associated with corruption. So if the inflation was, say $10$%, 2 percentage points can be attributed to corruption. Not small.

Braun, M. &amp; Di Tella R., (2004). Inflation, inflation variability, and corruption. Economics &amp; Politics, 16(1), 77-100.
They examine the reverse relationship: inflation facilitates corruption. They present a theoretical model, and also empirical evidence. For the theoretical model they write:


  "(...)high variability of inflation can make over-invoicing by
  procurement officers and under-invoicing by salespersons easier
  because it makes auditing more expensive to the principal".


So here there is a causative theoretical argument as to why unstable prices increase corruption.

Their data relates to 75 countries and for the period 1980-1994:


  Algeria, Argentina, Austria, Bahamas, Bahrain, Bangladesh, Belgium,
  Bolivia, Botswana, Burkina Faso, Cameroon, Canada, Chile, Colombia,
  Costa Rica, Cote d’Ivoire, Cyprus, Denmark, Dominican Republic,
  Ecuador, Egypt, El Salvador, Ethiopia, Finland, France, Gambia,
  Germany, Ghana, Greece, Guatemala, Haiti, Honduras, Hungary, India,
  Indonesia, Israel, Italy, Jamaica, Japan, Jordan, Kenya, Korea
  (South), Luxembourg, Madagascar, Malaysia, Malta, Mexico, Morocco,
  Myanmar, Netherlands, Niger, Nigeria,Norway, Pakistan, Paraguay, Peru,
  Philippines, Portugal, Senegal, Singapore, South Africa, Spain, Sri
  Lanka, Suriname, Sweden, Switzerland, Thailand, Togo, Trinidad and
  Tobago, Turkey, United Kingdom, USA, Uruguay, Venezuela, Zimbabwe.


Here the dependent variable is the corruption index. They use the International Country
Risk Guide (ICRG), that ranges from $0$ to $6$. Here too, a higher score means less corruption. They regress it (among various controls), on inflation variance (since what they want to test is whether an unstable price system introduces noise into transactions that facilitates corruption). They find statistically significant regression coefficients with values around $0.5$. They even find that inflation variability correlates more strongly with corruption, than inflation itself. Lots of references.

Dreher, A., &amp; Herzfeld, T. (2005). The economic costs of corruption: A survey and new evidence. Public Economics, 506001.
A more general study on the costs of corruption, looking also at inflation. For their empirical study (71 countries, 1975-2001), they also use the ICRG index. They regress the level of inflation on this index, and they find a positive sign on the coefficient. Since the index is as described above, a non-corruption index, higher values mean less corruption. So what they find is that less corruption is correlated with higher inflation. Irrespective of whether this can stand reason, their findings are also incredibly large: if you move up the ladder by one point in the ICRG scale (less corruption), the corresponding inflation will be 10 percentage points higher(i.e. if it was, say, 5%, it will become 15%). This is too large to be believable even if the direction of association is to be accepted. Despite this, this is a survey, so lots of references.  

Blackburn, K., &amp; Powell, J. (2011). Corruption, inflation and growth. Economics Letters, 113(3), 225-227.
This is a theoretical model. as the authors write:


  "We present a model in which the embezzlement of tax revenues by public
  officials leads the government to rely more on seigniorage to finance
  its expenditures. This raises inflation which depresses investment and
  growth via a cash-in-advance constraint."


So here we have a causative theoretical argument about why increased corruption causes increased inflation.

Bittencourt, M. (2012). Inflation and economic growth in Latin America: some panel time-series evidence. Economic Modelling, 29(2), 333-340.
Four Latin American countries (Argentina, Bolivia, Brazil, Peru) for the period 1970-2007. As the authors note, these four countries account for $\approx 70$% of total GDP and population in South America (for 2009). The dependent variable on their regressions is the growth rate, while both inflation and a composite "political situation" variable are included as regressors. The "political situation" variable again increases with increased transparency and controls on power, and so it can be expected to correlate negatively with corruption (i.e. the higher its value, the less corruption). For our purpose we need to look not at the regression results but at the correlation matrix of the regressors: there we see that the political situation variable is negatively correlated with inflation, with correlation coefficient $-0.142$ (so again, more corruption is associated with more inflation).

Overall, it appears that scholars have empirically detected a positive correlation between the level of corruption and the level of inflation, and also offered theoretical insights on how this can come about, although one theoretical model argues in favor of a causal effect from inflation to corruption, while the other from corruption to inflation. Since both arguments seem reasonable, one could think that it may be the case of a vicious feedback spiral.