Sydenham's Law of Public Expenditure and Economic Growth

Sydenham's Law: Significant increases in the growth of  public expenditure  accompany decreases in private sector growth.

What is the relationship between public spending and economic growth?  There are many theories but the surest way to observe the real effect is to examine the historical record and compare public expenditure with private sector growth.  If we look at the real data and do not rely on theories we discover that if you increase the growth of public spending you depress the economy.  This relationship is so consistent that it deserves to be called a "Law" of economics:

Sydenham's Law: Significant increases in the growth of  public expenditure  accompany decreases in private sector growth.

Sydenham's Law of public spending
and private sector growth

The diamond shapes due to Sydenham's Law are all over the public sector-private sector growth graphs.  The historical record is crystal clear: increasing public spending does not stimulate the private sector.  Look at the graphs below for the UK and US economies.

What is never seen is the theoretical "Keynesian event" where public spending increases growth.  In the past 60 years the UK has had several governments that believed in the Keynesian model but Keynesian events are not observed in the UK data despite their interventions.

Here are the data for the UK for the post war period with smoothing applied (click on graphs to enlarge them):

Graph 1: UK The effect of changes of public sector spending on the private sector

In the UK, rises in public spending appear to decrease the growth of the private sector.  When the red line goes up the blue line goes down and vice versa. Sydenham's Law applies in all cases: when public spending increases the private sector growth rate decreases.  It will be demonstrated below that Sydenham's Law is due to government incompetence as well as automatic regulation of the economy.

Notice that Keynesian events are never found in the data.  Keynesian interventions have either never occurred in the UK or Keynesian theory is wrong.  


The smoothing in graph 1 shows that the effect is not due to reporting intervals that are out of phase.  Notice how the abrupt policy change, the cut in spending in 2009-10, reversed the private sector decline.  (The unsmoothed data is given in Graph 7 below and is even more convincing).

One reason why government spending fails to cause growth is that it tends to be immediately devalued by inflation. The data for change in public spending versus inflation rate show the emptiness of using loans or printing money to increase economic performance:

Graph 2: UK: Annual increase in public spending and inflation
Yellow lines: inflation %, Red: increase in public spending % 

As can be seen, large increases in public spending are simply dissipated by inflation.  Just look at the absolutely massive cash injections by the government in the 1970's, all squandered by inflation.  This means that Sydenham's Law applies whatever the source of a government's spending - there is no magic government borrowing or printing of money that will fix everything.

The graph below shows the annual percentage change in public expenditure (inflation adjusted) versus growth in the private sector part of the economy in the USA since 1950:

Graph 3: USA: The effect of changes of public sector spending on the private sector

Notice that when the blue lines go up the red lines usually go down and vice versa.  As public expenditure increases non-public, private sector growth declines. (You can click on the graphs to make them bigger).

Sydenham's Law applies to both the US and UK economies. This is a "law" of economics because the two factors, public spending and private sector growth are tightly linked.  Does public sector growth control private GDP or private GDP growth control public spending?  This is discussed in Note 1 below and it seems that public spending growth controls private sector growth.

Sydenham's law also applies to Japan:

A recent massive increase in Japanese public spending has completely destroyed the private sector recovery that seemed to be happening in 2009-2010:

 (I do not have the raw data for 2011 and 2012).

Is Keynesianism rational?

It is interesting that the coupling between public spending and private sector output occurs when the public sector is at least about 10% of GDP and requires public spending of over 15-20% to become a "Law".  The USA provides an example of an economy that only reached a 10% tax take after the first world war.

Graph 4

Notice that the much vaunted "New Deal" in the mid 1930s seems to have followed and possibly reduced a larger private sector recovery.

Data for the New Deal period

Graph 5

There can be no doubt that the "New Deal" of 1934 benefited from a pre-existing recovery in the private sector.   The principle myth of Keynesianism, that public works stimulated the economy, is false.  In fact the public spending of the late 30s probably suppressed a greater recovery.

Inflation	Year	GDP-US $ billion nominal	Population-US million	Total Spending -total $ billion nominal	Non public GDP	Inflation Factor 1/(1+Inf'n)	Change in Public Spending	Change in Non-Public GDP
0.9%	1926	96.949	116.019	10.780	86.169	0.991	0.030	0.065
-1.9%	1927	95.544	117.775	11.220	84.324	1.019	0.061	-0.002
-1.2%	1928	97.365	119.557	11.440	85.925	1.012	0.032	0.031
0.0%	1929	103.600	121.366	11.680	91.920	1.000	0.021	0.070
-2.7%	1930	91.200	123.203	11.920	79.280	1.028	0.049	-0.114
-8.9%	1931	76.500	124.071	12.170	64.330	1.098	0.121	-0.109
-10.3%	1932	58.700	124.945	12.440	46.260	1.115	0.140	-0.198
-5.2%	1933	56.400	125.825	12.620	43.780	1.055	0.070	-0.002
3.5%	1934	66.000	126.712	12.810	53.190	0.966	-0.019	0.174
2.6%	1935	73.300	127.605	14.780	58.520	0.975	0.125	0.072
1.0%	1936	83.800	128.504	16.760	67.040	0.990	0.123	0.134
3.7%	1937	91.900	129.410	17.220	74.680	0.964	-0.009	0.074
-2.0%	1938	86.100	130.321	17.680	68.420	1.020	0.048	-0.065
-1.3%	1939	92.200	131.240	19.050	73.150	1.013	0.092	0.083
0.7%	1940	101.400	132.165	20.420	80.980	0.993	0.064	0.099

The changes are calculated as (Year2value x inflationfactor - Year1value)/Year1value
Data: US Bureau of economic Analysis: GDP and Other Major NIPA Series, 1929–2012:II,

www.usgovernmentspending.com ,Inflationdata.com, US Department of Labor CPI:  ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt

Notice that the improvement in private sector growth dates from 1932 but the New Deal started in 1934.

Analysis

This analysis does not mean that public spending should be slashed and slashed again.  It means that public spending should be carefully controlled so that it does not suppress growth. A modest growth in public spending that is less than the growth in the private sector part of GDP should be sustainable.  The UK can keep the NHS and welfare but great care must be taken not to overspend. You cannot simply spend your way out of a recession.

When there is an incipient recession government must not panic and increase public spending, in the UK, with almost 50% of the economy in the public sector, steady increases in the growth of public spending may briefly increase total GDP but they make the underlying problem worse by removing funds from the private sector.  If there is an incipient recession then public spending should be kept as steady as possible to pay for welfare (or even reduced) but public sector spending growth should not be increased until private sector growth returns.

The ideal for long term economic management is probably for public spending growth to change at a rate that is sufficiently low to have a minimal impact on GDP growth, this will probably avoid most recessions. 

It is probably true that government interventions smooth out some of the more extreme changes in GDP but, as will be seen below, they also cause extreme changes in the private sector.  The net effect of government interventions during downturns seems to be little more than a shift of value from the productive private sector to the non-productive state sector which exacerbates the downturn in the private sector.

Graph 6 USA GDP growth in yellow

The moral of Sydenham's Law is that governments should not fiddle about with the public finances. If more public spending is required just increase the public sector steadily, at the same constant rate per year, don't jerk around.

Governments should always have a surplus of about 3% of revenue over spending and increase revenues at a steady rate that is comparable to the long term growth in GDP with a target of spending being less than 40% of GDP.


Note 1: Does public spending control private sector growth or vice versa?

Public spending is almost certainly the causative agent.

It could be argued that public spending changes automatically with private sector growth, for instance declines in the private sector causing unemployment and hence more spending.  This "automatic regulation of the economy" cannot apply where private sector growth is greater than zero because the economy is growing, there is no increase in unemployment etc. In Graph 7 below there are changes that cannot be blamed on "automatic regulation of the economy", for instance, in 1971 there is a fall and in 1972 a massive rise in public spending when growth is buoyant, the fall in public spending causes a rise in private sector growth and the rise in spending a fall in growth.

In the data for the USA there are some large increases in public spending relating to the Vietnam War that correlate with reduced private sector growth rates, in the UK there are increases in spending due to Labour's ideological stance and Keynesianism that reduce private sector growth rates. These events show that deliberate increases in the rate of change of public spending cause decreases in private sector growth.

Graph 7: Unsmoothed UK data, notice how Brown's spending spree reduced growth.

(The full data for the UK is tabulated at the end of the article Is Labour right?,/>)

Public spending is clearly directly linked to private sector growth.  When public spending increases taxes are usually increased to pay for the spending.  These taxes remove money from the private sector and immediately reduce growth.  When there are tax cuts public spending is usually reduced and the private sector benefits immediately.

If public spending is increased as a result of loans or printing money then inflation increases, depressing the private sector and reducing the value of loans.  The only major exception to this pattern is Black Wednesday.

There is also a more subtle relationship between the growth of public spending and private sector growth that is due to the fact that the public sector does not trade, it does not add value.  If a company supplies another company with £10 worth of goods these may produce £20 of sales for the second company and so £20 of GDP in total may be generated, if a company sells £10 of goods to the government only £10 of GDP is generated.  It might be thought that £10 of GDP is better than nothing and this would indeed be true if the company that sold the goods to the government could use the money to increase its capacity and so increase sales to the private sector.  However, if public sector spending increases still further it will use up this spare capacity.  Any continuously increasing public spending will divert private sector resources to the public sector and may decrease private sector growth.

The influence of changes of private sector growth on public spending is less clear than the effect of public spending on the private sector part of GDP.  Decreases in Private sector growth often just leave the private sector growing at a slower rate, they do not necessarily cause unemployment or economic distress. So decreases in private sector growth will not always trigger immediate increases in public spending in the form of welfare payments etc.. Increases in private sector  growth are even less likely to have the observed effect on public spending.  The observed relationship is that increased private sector growth is related to decreased public sector growth but the increased tax take when private GDP is growing should have the opposite effect. It is clear that the private sector growth cannot be controlling public sector growth so it is deliberate government spending that is the controlling factor: increasing public spending depresses the economy.


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See also:

Public spending and GDP

Is Labour right?


The raw data for the USA:

Inflation	Year	GDP-US $ billion nominal	Population-US million	Total Spending -total $ billion nominal	Non public GDP
0.0%	1900	20.567	76.212	0.63	19.937
0.0%	1901	22.269	77.68	0.64	21.629
4.0%	1902	24.062	79.176	1.66	22.402
3.8%	1903	25.93	80.701	1.76	24.17
0.0%	1904	25.681	82.255	1.87	23.811
0.0%	1905	28.788	83.839	1.99	26.798
0.0%	1906	31.037	85.453	2.11	28.927
3.7%	1907	33.851	87.099	2.24	31.611
-3.6%	1908	30.133	88.776	2.38	27.753
0.0%	1909	32.229	90.486	2.53	29.699
3.7%	1910	33.423	92.229	2.68	30.743
0.0%	1911	34.343	93.523	2.85	31.493
3.6%	1912	37.384	94.836	3.03	34.354
2.4%	1913	39.14	96.167	3.21	35.93
1.3%	1914	36.479	97.516	3.49	32.989
0.9%	1915	38.675	98.885	3.79	34.885
7.7%	1916	49.638	100.273	4.08	45.558
17.8%	1917	59.702	101.68	5.67	54.032
17.3%	1918	75.835	103.107	16.76	59.075
15.2%	1919	78.333	104.554	22.96	55.373
15.6%	1920	88.393	106.022	11.33	77.063
-10.9%	1921	73.603	107.626	10.53	63.073
-6.2%	1922	73.432	109.254	9.3	64.132
1.8%	1923	85.414	110.908	9.63	75.784
0.4%	1924	86.947	112.586	9.98	76.967
2.4%	1925	90.575	114.29	10.37	80.205
0.9%	1926	96.949	116.019	10.78	86.169
-1.9%	1927	95.544	117.775	11.22	84.324
-1.2%	1928	97.365	119.557	11.44	85.925
0.0%	1929	103.6	121.366	11.68	91.92
-2.7%	1930	91.2	123.203	11.92	79.28
-8.9%	1931	76.5	124.071	12.17	64.33
-10.3%	1932	58.7	124.945	12.44	46.26
-5.2%	1933	56.4	125.825	12.62	43.78
3.5%	1934	66	126.712	12.81	53.19
2.6%	1935	73.3	127.605	14.78	58.52
1.0%	1936	83.8	128.504	16.76	67.04
3.7%	1937	91.9	129.41	17.22	74.68
-2.0%	1938	86.1	130.321	17.68	68.42
-1.3%	1939	92.2	131.24	19.05	73.15
0.7%	1940	101.4	132.165	20.42	80.98
5.1%	1941	126.7	133.966	24.35	102.35
10.9%	1942	161.9	135.792	45.58	116.32
6.0%	1943	198.6	137.643	92.71	105.89
1.6%	1944	219.8	139.519	109.95	109.85
2.3%	1945	223	141.421	118.18	104.82
8.5%	1946	222.2	143.349	79.71	142.49
14.4%	1947	244.1	145.303	57.73	186.37
7.7%	1948	269.1	147.283	55.08	214.02
-1.0%	1949	267.2	149.291	62.71	204.49
1.1%	1950	293.7	151.326	70.33	223.37
7.9%	1951	339.3	153.917	75.94	263.36
2.3%	1952	358.3	156.552	99.9	258.4
0.8%	1953	379.3	159.232	110.05	269.25
0.3%	1954	380.4	161.958	111.33	269.07
-0.3%	1955	414.7	164.731	110.72	303.98
1.5%	1956	437.4	167.551	115.8	321.6
3.3%	1957	461.1	170.42	125.46	335.64
2.7%	1958	467.2	173.337	134.73	332.47
1.0%	1959	506.6	176.305	145.75	360.85
1.5%	1960	526.4	179.323	151.29	375.11
1.1%	1961	544.8	181.588	164.83	379.97
1.2%	1962	585.7	183.881	169.5	416.2
1.2%	1963	617.8	186.204	177.35	440.45
1.3%	1964	663.6	188.555	189.11	474.49
1.6%	1965	719.1	190.937	193.89	525.21
3.0%	1966	787.7	193.348	216.22	571.48
2.8%	1967	832.4	195.79	248.07	584.33
4.3%	1968	909.8	198.263	277.19	632.61
5.5%	1969	984.4	200.766	296.09	688.31
5.8%	1970	1038.3	203.302	321.84	716.46
4.3%	1971	1126.8	205.515	354.79	772.01
3.3%	1972	1237.9	207.752	388.25	849.65
6.2%	1973	1382.3	210.013	411.64	970.66
11.1%	1974	1499.5	212.299	453.23	1046.27
9.1%	1975	1637.7	214.609	550.53	1087.17
5.7%	1976	1824.6	216.945	620.29	1204.31
6.5%	1977	2030.1	219.307	668.17	1361.93
7.6%	1978	2293.8	221.694	734.47	1559.33
11.3%	1979	2562.2	224.107	809.24	1752.96
13.5%	1980	2788.1	226.546	940.24	1847.86
10.3%	1981	3126.8	228.67	1073.12	2053.68
6.1%	1982	3253.2	230.815	1179.43	2073.77
3.2%	1983	3534.6	232.979	1283.58	2251.02
4.3%	1984	3930.9	235.164	1353.81	2577.09
3.5%	1985	4217.5	237.369	1496.29	2721.21
1.9%	1986	4460.1	239.595	1592.72	2867.38
3.7%	1987	4736.4	241.842	1662.02	3074.38
4.1%	1988	5100.4	244.11	1771.33	3329.07
4.8%	1989	5482.1	246.399	1915.12	3566.98
5.4%	1990	5800.5	248.71	2088.85	3711.65
4.2%	1991	5992.1	251.802	2230.3	3761.8
3.0%	1992	6342.3	254.933	2349.28	3993.02
3.0%	1993	6667.4	258.103	2420.82	4246.58
2.6%	1994	7085.2	261.312	2506.9	4578.3
2.8%	1995	7414.7	264.561	2634.73	4779.97
2.9%	1996	7838.5	267.85	2719.3	5119.2
2.3%	1997	8332.4	271.18	2813.4	5519
1.6%	1998	8793.5	274.552	2923.17	5870.33
2.2%	1999	9353.5	277.966	3053.31	6300.19
3.4%	2000	9951.5	282.172	3239.91	6711.59
2.8%	2001	10286.2	285.082	3428.55	6857.65
1.6%	2002	10642.3	287.804	3697.49	6944.81
2.3%	2003	11142.2	290.326	3934.54	7207.66
2.7%	2004	11853.3	293.046	4131.75	7721.55
3.4%	2005	12623	295.507	4397.1	8225.9
3.2%	2006	13377.2	298.109	4697.84	8679.36
2.9%	2007	14028.7	300.733	4923.25	9105.45
3.8%	2008	14369.1	303.38	5339.88	9029.22
-0.4%	2009	13939	306.051	5970.04	7968.96
1.6%	2010	14508.2	308.746	5942.98	8565.22
3.2%	2011	14958.6	311.592	6059.65	8898.95
1.7%	2012	15601.5	314.123	6231.69	9369.81

Data source