The death penalty as a deterrent to crime is ineffective is the prevailing view amongst researchers and experts in the field of criminology.
Some studies would indicate that there is no correlation between the death penalty and the reduction of violent crime. However, like any topic, you can find contrarian views that say there is no conclusive evidence to say that it does not. The increased use of econometric models is inconclusive aswell.
"The data alone cannot reveal what the homicide rate in a state without (with) a capital punishment regime would have been had the state (not) had such a regime."
"In their book, Professors Hood and Hoyle say almost all the academic studies available for review are concerned with the deterrent effect of capital punishment on the rate of murder in the United States.
The authors say theoretical and methodological issues have 'dogged the attempts to prove or disprove the existence of the deterrent effect of executions in the United States' and 'a fierce controversy continues' in the United States over attempts to use econometric models to address the question.
After reviewing the literature they conclude that 'it is not prudent to accept the hypothesis that capital punishment, as practised in the United States, deters murder to a marginally greater extent than does the threat and application of the supposedly lesser punishment of life imprisonment'."
"His position is shared by the majority of criminologists in relation to homicide, according to a 2009 survey of members of the American Criminology Society, who were asked to limit their answers to their understanding of the empirical research and to exclude their personal opinions. That study found that over 88 per cent of the criminologists did not believe the death penalty deterred murderers."
"A comprehensive review of the research in this area over 34 years was conducted in 2012 by a committee of the American National Academy of Sciences National Review Council. The committee concluded that "research to date on the effect of capital punishment on homicide is not informative about whether capital punishment decreases, increases, or has no effect on homicide rates"
Furthermore, as a penalty itself, the death penalty is morally repugnant and an anti-thesis to any government that would claim moral authority over its citizens.
Additionally, it is extremely costly as a form of punishment, some within the UN argue it can constitute torture and for its finality as a punishment, there is far too much human error involved in its delivery.
"From 1973 through December 2014, 150 innocent people were exonerated from death row"- https://www.aclu.org/issues/human-rights/human-rights-and-death-penalty
Then there are the issues within the legal institutions that would apply it, and the biases they hold.
• Jurors in Washington state are three times more likely to recommend a death sentence for a black
defendant than for a white defendant in a similar case. (Prof. K. Beckett, Univ. of Washington, 2014).
• In Louisiana, the odds of a death sentence were 97% higher for those whose victim was white than for those whose victim was black. (Pierce & Radelet, Louisiana Law Review, 2011).
• A study in California found that those convicted of killing whites were more than 3 times as likely to be sentenced to death as those convicted of killing blacks and more than 4 times more likely as those
convicted of killing Latinos. (Pierce & Radelet, Santa Clara Law Review, 2005).
In terms of economic analysis, I don't know if this is what you had in mind, but it is related, with cited research by economists who've endeavored to study the issue through that lens. Albeit from 1996
A small snippet from the above link - "In 1973, economist Isaac Ehrlich studied data from robberies that occurred in the 1940s,1950s, and 1960s. He found that the higher the probability of conviction for robbery, the
lower the robbery rate, ceteris paribus (Cooter and Ulen 1988). However, he found that the severity of the punishment did not affect deterrence in 1940 and 1960. Interestingly, he found a deterrent effect based on the severity of punishment when studying robbery reports from 1950. More recently the Capital Punishment Research Project and the New York Times compared capital and non-capital states to assess deterrence effects (Economist 1994a).The investigation examined the number of murders that occurred in New Jersey before and after the imposition of a death penalty statute in 1982. No statistically significant decrease was found in the number of murders that occurred. The study also compared the number of murders per 100,000 residents in both Massachusetts (a non-capital state) and New Jersey (presently a capital state). No significant difference was found in the number of murders. In the same study, the murder rate in New York (a non-capital state when the study was conducted) was compared to the rate in Texas (a capital state); and there was no statistical difference between the two states with respect to the number of murders per 100,000 residents. Interestingly, while most southern states have the death penalty, they also have higher murder rates. In fact, Louisiana, a capital state, has the highest murder rate in the nation. Among southern states, only Florida has a murder rate below the national average"
In terms of overall views on the subject, it differs highly in which country you are referring to, as it is not just a scientific issue, but a political one. There is also unfortunately a lot of ignorance and emotionally distorted reasoning when dealing with the topic with those unfamiliar with it.