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I am running a simple correlation and scatter plots similar to the one here between the unemployment rate as the outcome variable, as unemployment insurance UI claims as the independent variable. I only have 34 observations (i.e. periods) so I assume I can't run a regression analysis, correct?

If I am interested in learning whether changes in UI claims help us in predicting future changes in the unemployment rate, shall I run the correlation on data for the two indicators as shown below OR should the correlation be between changes in the two variables?

Data example:

urate   UI claims
11.6    3516
12.1    3869
12.3    12007
12.7    10300
12.8    6975
12.8    5880
12.8    8355
12.9    9946

By changes in the two variables, I mean computing the monthly difference/changes in unemployment and UI claims, and then running the correlation on this data:

change_urate.  change_UIclaims
0.5              353
0.2.             8138
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    $\begingroup$ In practice, there won't necessarily be a direct relationship between the changes. For instance, there could be a delay in time between when one value changes and when the other changes (even without being causal). There could even be effects strictly within one of the factors, such as claims being cut off after say 6 months, which would result in the claims value having a sudden drop 6 months after it had a sudden rise. $\endgroup$
    – Ray Butterworth
    Commented Jul 3, 2023 at 13:07
  • $\begingroup$ Correct, depending on the economic context. For instance, I have noticed that the the impact of increasing UI claims appears 3-5 months on the U-rate in California. This is because during the first few months of unemployment, most individuals aren't actively looking for a job and are thus not captured in the official U-rate. However, as UI benefits decline, more individuals start actively searching for a new job, which thus leads to them being counted in the U-rate. $\endgroup$
    – maldini1990
    Commented Jul 3, 2023 at 13:12

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so I assume I can't run a regression analysis, correct?

Incorrect, there is no such requirement for linear regression (or a correlation coefficient).

If I am interested in learning whether changes in UI claims help us in predicting future changes in the unemployment rate

If you are interested in the relationship between the changes then you need to model the changes, if you are not interested in the changes then don't look at changes. Also, since this is observational data, do not try to make (too many) inferences about causality.

(Made-up) Should I analyze the relationship between the original variables or the changes? What about logs?

That is a different question. This is time series data, looking at the original variables as-is is likely to be misleading, it is probably necessary to process the data somehow. Are (monthly or some other aggregation) lagged differences enough? I don't know, I don't have the data. Logs might help.

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  • $\begingroup$ Thanks for the suggestion. Indeed, I am planning to use a log-transformed function of UI claims, similar to prior work on this area. On the minimum number of observations for regression analyses, based on the source below, it seems that 10 per variable is the rule of thumb, thoughts? stats.stackexchange.com/questions/37833/… $\endgroup$
    – maldini1990
    Commented Jul 3, 2023 at 12:50
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    $\begingroup$ @nesta1992 I wouldn't get too bogged down with such rules as they are very much problem-specific. The coefficient estimates will tell you how uncertain the model is about the results, you can use these to determine if your sample is trust-worthy (that is if you are happy with the uncertainty). $\endgroup$
    – user2974951
    Commented Jul 3, 2023 at 12:56

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