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This rebuttal of criticism of your work is sound from a technical stance, but does not address the issue of interpretation. Please let me explain via an analogy the issue, not with the analysis you have undertaken itself, but with the interpretation of your findings, which I feel undervalues the role NHS finance professionals play in terms of forecasting financial issues on the horizon and acting to mitigate their worst effects.

Before diving into this analogy make it very clear that I have no issue whatsoever with your approach from a technical stance. This includes your use of alternative variables and time lagging of variables. I would also note that your original article was very transparent in pointing out data limitations and the ways in which you attempted to handle these was again in line with what I’d expect.

Your findings are essentially as follows:
1. Increases in management consultancy spend are correlated with increases in cost (controlling for other variables) in the year in which the consultancy spend happens.
2. Also, increases in management consultancy spend are correlated with increases in cost (controlling for other variables) in the year after the consultancy spend happens. This provides some comfort that there is some form of predictive causality between the two variables.
3. When swapping your original Y variable (RCI) for a different one you still find the same pattern.
4. Based on this you infer that consulting spend results in increased cost.

An analogy
1. The use of snow tires in Scandinavia is correlated with snow fall
2. Scandinavians fit snow tires in a period before the snow falls (the same basis for which you infer causality)
3. Swapping Y variables, Scandinavians also fit snow tires before a drop in the temperature.
4. Based on your logic, snow tires cause snow and cold weather (because otherwise they would have fit the tires after it snowed, not before).

What is missing from your interpretation is an understanding of human behavior and the ability to forecast. Just as people use past experience and weather forecasts to predict snow (and prepare for it by fitting snow tires), it is my experience that NHS finance teams have a very good idea when their organisation is about to fall into financial difficulty. This may be because they are good at forecasting, because they know of a particular pressure which is about to hit, or because they have been using non-recurrent means to prop up their financial position and their scope to do this has run out. It is in this circumstance trusts often bring in consultants. Much like snow tires, using consultants doesn’t stop the forecast snow from falling, or the temperature from dropping, but mitigates some of its worst effects.

So as I said earlier, the issue is not with your statistical approach, but with your interpretation of your findings and the lack of credit you give NHS finance professionals in their ability to forecast trouble ahead.