Rising GDP per capita can coincide with deflation and falling government spending

According to the Keynesian theory of macroeconomics, one justification for expansionary monetary policy is that prices (and particularly wages) are sticky downwards, meaning that they may not adjust appropriately when demand drops during a recession. To quote the estimable Tim Harford:

Sticky prices. Think about it. If prices adjusted with complete freedom in response to competitive forces, then the actual amount of currency in an economy simply would not matter.

Expansionary monetary policy reduces the value of the currency, which allows prices to fall without their nominal value changing. A key prediction of this theory is that recessions should take much longer to recover from in the absence of either expansionary monetary policy or expansionary fiscal policy funded through borrowing. Indeed, the fact that most countries, such as the UK and the US, have had massive secular inflation since the early the 20th century is a testament to how influential the theory has been. 

In this context, it is interesting to note that between about 1815 (when Wellington's victory at Waterloo brought an end to the Napoleonic wars) and about 1850, Britain experienced rising GDP per capita, deflation and falling government spending. The first chart (below) plots GDP per capita in Britain between 1700 and 1850, using data from the Maddison Project (which are not reported for Britain after 1850). The second chart, which is taken from a parliamentary report on the historical value of the pound, plots the retail prices index between 1750 and 2011 (on a log scale). And third chart, which is taken from Gregory Clark's book A Farewell To Alms, plots government spending as a percentage of GNP in England between 1285 and 2000. 

The three respective charts show that, between about 1815 and about 1850: GDP per capita took an unmistakably upward trend; the retail prices index declined in a haphazard fashion and then roughly stabilised; and government spending as a percentage of GNP collapsed from ~30% to ~18% before decreasing further to ~12%. Prima facie, these observations would seem to be inconsistent with Keynesian theory. 

Five possible explanations are as follows. First, all three series contain too much measurement error to be reliable. Second, output per capita didn't actually grow that fast: only ~1% per year on average. Third, output per capita increased simply because of "pent up demand" from the period encompassing the Napoleonic wars. Fourth, prices tend not to be quite as sticky when the economy is smaller and less complex. Fifth, prices tend not to be quite as sticky when there are fewer labour market regulations. I'd be interested to know if anyone has another explanation or would argue that the data are in fact perfectly consistent with Keynesian theory.