Issue with lagged models

[Loris Di Stefano]

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:

reg popdensity EQ $control, vce(cluster provcode)

So I modeld the regression with lags and leads (and fixed effects etc.) this way:

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))

* 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

[Loris Di Stefano]

In the meantime, if someone is interested, I found a satisfying answer to question 1. in a paper by Kai Gehring for the UZH:


"In this case, our theoretical considerations suggest that the Commissioners are able to affect budget allocation in favor of their home country only once they are in office. A positive and significant lead-variable would thus cast doubts on the causal interpretation of our earlier results as it would indicate different trends between treated and untreated countries. Significant lags are theoretically possible and not implausible; the Commissioners could either install staff that support their cause even after their dismissal or change internal processes or rules which take some time to reverse. Additionally even once agreed upon, implementing a policy change usually takes some time."


Gehring, Kai and Schneider, Stephan A., Towards the Greater Good? EU Commissioners’ Nationality and Budget Allocation in the European Union (February 23, 2016). Zürich CIS Working Paper No. 86. Available at SSRN: https://ssrn.com/abstract=2742607 or http://dx.doi.org/10.2139/ssrn.2742607

[Phil Bromiley]

What does it mean if in my results the coefficient for a lag is significant? - normally we only lag variables - things take time to influence dv's very often. Leads are much less common and often open up endogeneity problems.
So, interpretation is 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 [Stata please] to infer the long-run effects on the population density of said municipality?

Without lagged dv's, I'm not sure where you get a different long run than short run effect.

[Loris Di Stefano]

well, let's say my short run model looks like this:

Y_i,t= α + β₀ X_i,t + ε<sub>i,t

Then by adding lags for the indep. var. X the model looks like:</sub>

Y_i,t= α + β₀X_i,t + β₁X_i,t+1 + β₂X_i,t+2 + β₃Xi,t +3 ... + βnXi,t + ε<sub>i,t

So isn't the long run relationship between Y and X given by:</sub>

Y_i,t= α + (β₀+ β₁ + β₂+ β₃ ... + βn) X_i,t

???

How do I model that in Stata without having to add the effects of the lags together by hand? Is there a command that does that?