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I've been working with some historical macroeconomic data of the Canadian economy and am having difficulty empirically testing the Phillips curve long run and short run versions.

I got the data from FRED, logged the variables and then plotted them.

The results are unsatisfactory; the scatter plot I have is:
enter image description here

A shape which is looking like a bow, going up right and then back.

I tried using fitting the data using a loess curve again yielding unsatisfactory results.enter image description here

Im probably not doing something right as the data does not seem to fit with either the short run or long run versions of what the Phillips curve represents.

So to offically crown myself as conspiracy theorist of the day on Economics.SE (which is probably a problem for a mod):

Does this analysis disprove both the long run and short run Phillips curve?

*for Canada?
** what is incorrect in this analysis?

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    $\begingroup$ Did my answer make sense? $\endgroup$ – luchonacho Oct 19 '17 at 19:55
  • $\begingroup$ @luchonacho conceptually it does, however the whole "loopty loop" charts I really don't get. All it does is leave me scratching my head. $\endgroup$ – EconJohn Oct 19 '17 at 20:01
  • $\begingroup$ @luchonacho I'll try to replicate the model which the bank of canada uses $\endgroup$ – EconJohn Oct 19 '17 at 20:03
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You are assuming the PC has not shifted over the period. For example, you can see at the top right some sort of PC. To see this better, you need first to analyse the data in evidence for regime shifts. The first suggestion is to connect the points over time. US example below:

enter image description here

This will let you see possible structural changes in the PC, together with movements between two PCs. This gif shows this more clearly:

enter image description here

Knowing the monetary and economic history of Canada should certainly help you understand the movement and changes of the PC. For example, you cannot expect the PC to hold over the oil crisis period, where the economy was basically in stagflation.

Once you identify sub-periods, estimate the PC for each subperiod.

A paper from the Central Bank of Canada estimating the PC and its regime shifts can be found here. Notice that standard analysis of PC are much more elaborated than a simply bivariate correlation. Strictly speaking, you are assuming there is no other variable involved in the correlation. The example of structural changes might for example be captured with changes in a variable you are omitting.

PS: I gave an answer to a related question here.

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