Correlation between variables over time in panel data

[Josh Dyson]

How do I go about displaying the change in correlation between two variables over time? I have a panel dataset with 30 years and several thousand firms. I would like to display graphically the change in the relationship between borrowing and investment over time. Many thanks!

[Nick Cox]

With that many companies you could calculate the instantaneous correlation, some lagged correlation, a correlation pooling results in some moving time window, and so on and so forth.

Without any pretence on my part that this makes economic or financial sense, here is an example using rangestat from SSC to show technique:

. webuse grunfeld, clear

. rangestat (corr) mvalue kstock, int(year 0 0)

. tabdisp year, c(corr_*)

------------------------------------------------------
     Year |            corr_nobs                corr_x
----------+-------------------------------------------
     1935 |                   10            -.24964919
     1936 |                   10            -.13778091
     1937 |                   10             .22234782
     1938 |                   10             .38337192
     1939 |                   10             .30699455
     1940 |                   10              .2418253
     1941 |                   10             .32405812
     1942 |                   10             .40219129
     1943 |                   10             .26078395
     1944 |                   10             .06473613
     1945 |                   10             .11464911
     1946 |                   10             .27747902
     1947 |                   10              .6398159
     1948 |                   10             .69484476
     1949 |                   10             .74271262
     1950 |                   10             .74092512
     1951 |                   10              .7555348
     1952 |                   10             .82361111
     1953 |                   10             .88239901
     1954 |                   10             .89396833
------------------------------------------------------

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