Estimating linear growth model

[Kartiki Verma]

Hi, I estimated a linear growth model in STATA and for this, I took the natural log of my dependent variable and declared the trend variable as time using "tsset" command. I regressed the equation of ln(dependent variable) on the trend variable using an OLS regression and created a graph to observe the growth rate of my dependent variable over time using the command "tsline". However, I faced two problems, first, my coefficient of trend variable is coming out to be insignificant, and second, the graph that I got is not monotonically increasing, it is coming up as a zig-zag line (first increasing then decreasing, and so on) which is quite hard to interpret. What should I do to get some significant results? what can I do to get an interpretable graph and How can I improve?
I hope I explained my questions well and thanks in advance for the help.

[George Ford]

the linear growth model is

ln(y) = a + b*t

You'll get a single coefficient. If it is not trending, then b will be insignificant (which appears to be your case). Sounds like you don't have a monotonically trending series, so the linear fit will be poor.

There is no graph of the growth rate over time. The linear trend fits to all the data. There is a growth rate, not rates.

There are ways to get different growth rates over time, but your approach is not it.