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Issue with lagged models

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Dear Statalist community,

I am executing a Diff-in-diff estimation.

My data is on the municipal-level and comprises the years 1936-2011.
Municipal-year-level observations;
Municipality:= 1,..,1442;
year:= 1936,..,2011.


My treatment:
around 450 Municipalities were struck by a seismic event of major force:
I expect the municipalities affected by such an event to display lower population density growth in the long-run.


My dependent variable: population density / population density growth = popdensity
My independent variable: dummy for earthquake presence in municipality m and year t = EQ


My baseline regression:

Code:
reg popdensity EQ $control, vce(cluster provcode)
So I modeld the regression with lags and leads (and fixed effects etc.) this way:

Code:
xtreg popdensity f2_EQ f1_EQ EQ l1_EQ l2_EQ l3_EQ  $control i.Year#i.regioncode, fe cluster(provcode)


My Questions:

1.
What does it mean if in my results the coefficient for a lag is significant?
that the treatment was anticipated and the population density was sinking/rising even before ?
Or that the treatment has delayed effects on the population density?

2.
I have data for each year so the coefficient of my earthquake dummy reflects the effect on population density of the next year...
Is there a model or command in stata to infer the long-run effects on the population density of said municipality?

Here an example of my dataset for one Municipality (Avezzano in this case (lovely village in central Italy))

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input int Year str43 Municipality float(f2_EQ f1_EQ EQ l1_EQ l2_EQ)
1936 "AVEZZANO" 0 0 0 . .
1937 "AVEZZANO" 0 0 0 0 .
1938 "AVEZZANO" 0 0 0 0 0
1939 "AVEZZANO" 0 0 0 0 0
1940 "AVEZZANO" 0 0 0 0 0
1941 "AVEZZANO" 0 0 0 0 0
1942 "AVEZZANO" 0 0 0 0 0
1943 "AVEZZANO" 0 0 0 0 0
1944 "AVEZZANO" 0 0 0 0 0
1945 "AVEZZANO" 0 0 0 0 0
1946 "AVEZZANO" 0 0 0 0 0
1947 "AVEZZANO" 0 0 0 0 0
1948 "AVEZZANO" 0 0 0 0 0
1949 "AVEZZANO" 0 0 0 0 0
1950 "AVEZZANO" 0 0 0 0 0
1951 "AVEZZANO" 0 0 0 0 0
1952 "AVEZZANO" 0 0 0 0 0
1953 "AVEZZANO" 0 0 0 0 0
1954 "AVEZZANO" 0 0 0 0 0
1955 "AVEZZANO" 0 0 0 0 0
1956 "AVEZZANO" 1 0 0 0 0
1957 "AVEZZANO" 0 1 0 0 0
1958 "AVEZZANO" 0 0 1 0 0
1959 "AVEZZANO" 0 0 0 1 0
1960 "AVEZZANO" 0 0 0 0 1
1961 "AVEZZANO" 0 0 0 0 0
1962 "AVEZZANO" 0 0 0 0 0
1963 "AVEZZANO" 0 0 0 0 0
1964 "AVEZZANO" 0 0 0 0 0
1965 "AVEZZANO" 0 0 0 0 0
1966 "AVEZZANO" 0 0 0 0 0
1967 "AVEZZANO" 0 0 0 0 0
1968 "AVEZZANO" 0 0 0 0 0
1969 "AVEZZANO" 0 0 0 0 0
1970 "AVEZZANO" 0 0 0 0 0
1971 "AVEZZANO" 0 0 0 0 0
1972 "AVEZZANO" 0 0 0 0 0
1973 "AVEZZANO" 0 0 0 0 0
1974 "AVEZZANO" 0 0 0 0 0
1975 "AVEZZANO" 0 0 0 0 0
1976 "AVEZZANO" 0 0 0 0 0
1977 "AVEZZANO" 0 0 0 0 0
1978 "AVEZZANO" 0 0 0 0 0
1979 "AVEZZANO" 0 0 0 0 0
1980 "AVEZZANO" 0 0 0 0 0
1981 "AVEZZANO" 0 0 0 0 0
1982 "AVEZZANO" 0 0 0 0 0
1983 "AVEZZANO" 0 0 0 0 0
1984 "AVEZZANO" 0 0 0 0 0
1985 "AVEZZANO" 0 0 0 0 0
1986 "AVEZZANO" 0 0 0 0 0
1987 "AVEZZANO" 0 0 0 0 0
1988 "AVEZZANO" 0 0 0 0 0
1989 "AVEZZANO" 0 0 0 0 0
1990 "AVEZZANO" 0 0 0 0 0
1991 "AVEZZANO" 0 0 0 0 0
1992 "AVEZZANO" 0 0 0 0 0
1993 "AVEZZANO" 0 0 0 0 0
1994 "AVEZZANO" 0 0 0 0 0
1995 "AVEZZANO" 0 0 0 0 0
1996 "AVEZZANO" 0 0 0 0 0
1997 "AVEZZANO" 0 0 0 0 0
1998 "AVEZZANO" 0 0 0 0 0
1999 "AVEZZANO" 0 0 0 0 0
2000 "AVEZZANO" 0 0 0 0 0
2001 "AVEZZANO" 0 0 0 0 0
2002 "AVEZZANO" 0 0 0 0 0
2003 "AVEZZANO" 0 0 0 0 0
2004 "AVEZZANO" 0 0 0 0 0
2005 "AVEZZANO" 0 0 0 0 0
2006 "AVEZZANO" 0 0 0 0 0
2007 "AVEZZANO" 0 0 0 0 0
2008 "AVEZZANO" 0 0 0 0 0
2009 "AVEZZANO" 0 0 0 0 0
2010 "AVEZZANO" . 0 0 0 0
2011 "AVEZZANO" . . 0 0 0
end
format %ty Year

As always thank you very much for your support/help in advance!

Kind regards,
Loris

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