# How to analyze Time-Series data?

I am currently writing my masters thesis and have some difficulties with the statistical part of my research. I am new here, with limited knowledge in econometrics.

I want to analyse the relationship between two variables.

1. R&D Expenses (in dollars, in a specific industry)
2. Number of Employees (in a specific industry).

The data represents a specific industry in a certain country. I have values for both variables on each consecutive year (2000 till 2013).

IV: Innovation (R&D), DV= Number of employees

This is what I have in mind, and thus, I want to analyze the impact of innovation on the number of employees in the industry.

My questions:

1. I have limited amount of data, would these consecutive 14 years be enough data to statistically research this?
2. Should I collect and use the accumulated values of a few countries for the analysis.
3. Should I do the analysis a few times for different industries?
4. How do I go about actually analyzing the relationship between the two, and more specifically the impact of innovation on number of employees? I am thinking of, what methods to use and what kind of tests to do?

I hope I was clear enough, please ask for further details. Thank you very much in advance!

• I think the tricky thing will be how to deal with the simultaneity issue. For example, research may alter employment, but it is also the case that researcher/staff salaries (an expense) are mechanically connected to number of employees, though that is not the effect you care about. Or you might have a growing company that is doing well and decided to invest in research because it can afford to do it or it helps with recruiting, but that growth is causally unrelated to the underlying research. I think having multiple countries and industries may open up some other possibilities. Sep 28 '17 at 17:11
• I want to comment on the first question- You have 14 repeated annual measures of an industry sector in a country. The main question I have is: are these observations at the country level? If you only have 14 total observations, you can definitely fit some kind of model to describe the correlation between your dependent and independent variable, but its level of usefulness on drawing inference will be limited. Another point to mention is that there is likely to be autocorrelation in your dataset, which violates one of the assumptions of a simple linear model. This means that for any given year, Sep 28 '17 at 17:21
• Thank you all for your comments and links which gave me a lot of insight. Unfortunately, my supervisor is not really responsive. I take that I have to look for more data. I think then, 30 values for each should suffice for increased usefulness. I am thinking about taking the data of several countries for certain industries. The industries will have separated, repeated analyses, but I think I should accumulate all values of "R&D expenses" and "number of employees" for all countries. This way, I will find out more about the overall impact of the variables. Any thoughts? Thank you! Sep 29 '17 at 13:23

Okay, I am not an econometrician, but if I hear econometrics and time-series, my first reaction is using Time-Series Regression . Here is a short example that appears to be comparable to your goal (Take note of the warning in the link and the other answer to your question about autocorrelation).

1. Regardless of what method you chose, 14 observations might be a bit low to get a useful model. If possible, try to get a bigger sample size. If that's all the data available to you, you still can use it, but point the lack of data as possible problem out when writing your thesis. Some discussion on how to estimate the usefulness of your model can be found here

2. depends on what you want to find out. I would assume that the effect depends on the country you examine. So it might be interesting to look at those time series separately and compare them

3. Sure, looking at different industries should give interesting results.
4. as answered above, I would look into such kind of models using distributed lag (a deeper explanation can be found here). they return coefficients that can be analyzed for the effect of each variable

Edited to fix some misunderstanding of the used terminology

• another sidenote: Aren't those the kind of questions, that your supervisor is there to discuss with you? Sep 28 '17 at 14:42
• Sometimes checking the tag infos can be helpful to understand the terms: here is the autocorrelation tag info, and here is the autoregresive tag info. Sep 28 '17 at 16:52
• I know the common interpretation of autocorrelation. But if you look into the first link I provided, some econometricians seem to use the term autocorrelation to refer to something that looks more like common regression, with some time-lagged terms. That's why I added the sidenote, because the method in the link is called autocorrelation and doesn't fit the normal definition of autocorrelation. Sep 28 '17 at 17:04
• Hm, OK. Could you cite precisely the relevant statement(s)? I could not see it in the first quick reading. Sep 28 '17 at 17:07
• Oh, that's quite embarrassing. On my first quick glance , I thought the author would use the term autocorrelation to describe the time-lagged models featured in that link, so I assumed he is using the term differently than I do. but he obviously doesn't do that. I have to edit my answer in that regard Sep 28 '17 at 17:21