I want to estimate a count data model (the dependent variable is patents count) with a continuous diff-in-diff specification ("natural experiment"). I have a small sample (N=16, T=30). The main regression is:
In one of the robustness checks, I would like to instrument my treatment variable. My IV (like my treatment) is time invariant. Currently, I'm using the following command
However, I saw in previous posts that this estimator might not be consistent (due to incidental parameters problem). I would be happy to get suggestions about the right direction. (In an old post, Jeff Wooldridge suggested: "to add the fixed effects residuals obtained in the first stage to the FE Poisson estimation in the second stage". I'm not sure if it works when the instrument is time-invariant and in general how exactly to implement that method (e.g., how to calculate the standard errors)).
Code:
gen treatment_post=treatment*post xtpoisson patents treatment_post i.year,fe vce(robust)
Code:
gen iv_post=iv*post ivpoisson gmm patents (treatment_post=iv_post) i.year i.group, vce(robust)
Code:
* Example generated by -dataex-. To install: ssc install dataex clear input byte group int year float post double(patents treatment) float iv 2 1971 1 3 .19008264462809918 14.162823 2 1964 0 1 .19008264462809918 14.162823 2 1962 0 1 .19008264462809918 14.162823 2 1951 0 0 .19008264462809918 14.162823 2 1955 0 0 .19008264462809918 14.162823 2 1970 1 3 .19008264462809918 14.162823 2 1978 1 0 .19008264462809918 14.162823 2 1954 0 1 .19008264462809918 14.162823 2 1968 1 3 .19008264462809918 14.162823 2 1948 0 2 .19008264462809918 14.162823 2 1977 1 0 .19008264462809918 14.162823 2 1973 1 2 .19008264462809918 14.162823 2 1950 0 1 .19008264462809918 14.162823 2 1960 0 0 .19008264462809918 14.162823 2 1979 1 1 .19008264462809918 14.162823 2 1972 1 1 .19008264462809918 14.162823 2 1963 0 0 .19008264462809918 14.162823 2 1984 1 1 .19008264462809918 14.162823 2 1981 1 1 .19008264462809918 14.162823 2 1983 1 1 .19008264462809918 14.162823 2 1974 1 2 .19008264462809918 14.162823 2 1949 0 0 .19008264462809918 14.162823 2 1965 1 3 .19008264462809918 14.162823 2 1980 1 1 .19008264462809918 14.162823 2 1957 0 0 .19008264462809918 14.162823 2 1958 0 0 .19008264462809918 14.162823 2 1953 0 2 .19008264462809918 14.162823 2 1966 1 6 .19008264462809918 14.162823 2 1956 0 0 .19008264462809918 14.162823 2 1967 1 2 .19008264462809918 14.162823 2 1961 0 2 .19008264462809918 14.162823 2 1975 1 3 .19008264462809918 14.162823 2 1982 1 2 .19008264462809918 14.162823 2 1985 1 0 .19008264462809918 14.162823 2 1952 0 1 .19008264462809918 14.162823 2 1976 1 1 .19008264462809918 14.162823 2 1969 1 3 .19008264462809918 14.162823 2 1959 0 1 .19008264462809918 14.162823 4 1973 1 0 .3243243243243243 13.913777 4 1969 1 1 .3243243243243243 13.913777 4 1976 1 0 .3243243243243243 13.913777 4 1953 0 0 .3243243243243243 13.913777 4 1979 1 4 .3243243243243243 13.913777 4 1956 0 0 .3243243243243243 13.913777 4 1958 0 0 .3243243243243243 13.913777 4 1963 0 0 .3243243243243243 13.913777 4 1978 1 0 .3243243243243243 13.913777 4 1977 1 1 .3243243243243243 13.913777 4 1974 1 0 .3243243243243243 13.913777 4 1961 0 1 .3243243243243243 13.913777 4 1966 1 1 .3243243243243243 13.913777 4 1980 1 0 .3243243243243243 13.913777 4 1955 0 1 .3243243243243243 13.913777 4 1965 1 1 .3243243243243243 13.913777 4 1982 1 0 .3243243243243243 13.913777 4 1975 1 0 .3243243243243243 13.913777 4 1967 1 3 .3243243243243243 13.913777 4 1957 0 0 .3243243243243243 13.913777 4 1949 0 2 .3243243243243243 13.913777 4 1951 0 0 .3243243243243243 13.913777 4 1968 1 1 .3243243243243243 13.913777 4 1972 1 0 .3243243243243243 13.913777 4 1954 0 0 .3243243243243243 13.913777 4 1981 1 0 .3243243243243243 13.913777 4 1950 0 1 .3243243243243243 13.913777 4 1960 0 0 .3243243243243243 13.913777 4 1971 1 0 .3243243243243243 13.913777 4 1985 1 0 .3243243243243243 13.913777 4 1962 0 0 .3243243243243243 13.913777 4 1983 1 0 .3243243243243243 13.913777 4 1952 0 0 .3243243243243243 13.913777 4 1970 1 0 .3243243243243243 13.913777 4 1984 1 0 .3243243243243243 13.913777 4 1959 0 2 .3243243243243243 13.913777 4 1964 0 0 .3243243243243243 13.913777 4 1948 0 1 .3243243243243243 13.913777 5 1979 1 3 .216072545340838 12.584287 5 1951 0 0 .216072545340838 12.584287 5 1968 1 9 .216072545340838 12.584287 5 1963 0 0 .216072545340838 12.584287 5 1948 0 3 .216072545340838 12.584287 5 1960 0 6 .216072545340838 12.584287 5 1952 0 0 .216072545340838 12.584287 5 1955 0 1 .216072545340838 12.584287 5 1985 1 2 .216072545340838 12.584287 5 1949 0 0 .216072545340838 12.584287 5 1974 1 14 .216072545340838 12.584287 5 1969 1 15 .216072545340838 12.584287 5 1978 1 0 .216072545340838 12.584287 5 1967 1 18 .216072545340838 12.584287 5 1982 1 2 .216072545340838 12.584287 5 1966 1 24 .216072545340838 12.584287 5 1984 1 1 .216072545340838 12.584287 5 1964 0 3 .216072545340838 12.584287 5 1975 1 4 .216072545340838 12.584287 5 1956 0 1 .216072545340838 12.584287 5 1983 1 2 .216072545340838 12.584287 5 1971 1 2 .216072545340838 12.584287 5 1981 1 0 .216072545340838 12.584287 5 1959 0 1 .216072545340838 12.584287 end
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