553 Class Note for ECON 570 at PSU
553 Class Note for ECON 570 at PSU
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Date Created: 02/06/15
Notes on Investment and Investment Prices Econ 570 Spring 2005 1 Introduction A very robust nding is that the investment rate is highly correlated with income 0 Mankiw et al nd that differences in investment rates account for around half of the income disparity across countries using the Solow type model 0 Levine and Renelt nd the investment rate as the lone robust correlate with growth in income per person using the standard Barro type regression1 o DeLong and Summers nd that it is machinery investment that is key2 in quotIndia like in Argentina the savings is relatively high but equipment is expen sivelndia demonstrates not that boosting investment is unproductive but that policies that boost saving while simultaneously raising the relative price of invest ment in equipment and structures are unproductive We suspect that restrictions on imports of capital goods have ensured that the Indian government s attempts to support investment have had effects not on quantities but on prices lndia s policies have managed to enrich industrialists instead of encouraging industry quot o Richer countries invest more than poorer countries This is clear from gure 1 Notice that PPP investment rates are 2 3 times higher for US and Norway compared with poor 1A standard Barroetype regression is a crossecountry regression of pericapita income growth over some period Dyt on a host of variables Dyt Oz 51yy71 th71 711t 72 5t where h is educational attainment and the 35 s are various policy variables such as the investment ratio corruption openness in ation rate democracy rule of law etc 2De Long and Summers 1 396 stress the distinction quotbetween investment effort 7 share of national product saved plus capital in ows 7 and investment 7 buildings constructed and machines put into productive use Many of the policies that have been followed in the posteWWH period especially in the developing world seem designed to maximize 7investment effort7 while ensuring that each unit of 7investment effort7 translates into as little actual investment as possiblequot Like so many other aspect of economic policy what was merely a disease in developing countries was a pathology in the socialist world Investment Ratios Spring 2004 countries like Mali and Kenya Thus both faster growing and richer countries invest more than slow growing and or poor countries 0 How does this t with the nding that TFP is what really matters What explains these nding 0 One set of arguments focuses on low savings rates and the F H hypothesis Classical low savings theories 0 Another set of arguments focuses on distortions to investment In particular it is pointed out that the relative price of investment is higher in poor countries This could be because of taxes or other distortions that make investment more expensive It could re ect trade policies barriers to entry prohibitions corruption and all sorts policy distortions that make investment more expensive the classic reference is to Argentina where the price of capital may have doubled in the Peron era 10 Price Distortions and the Lucas Puzzle Recall the Lucas puzzle 7 with common technologies and 04 4 India has a marginal product of capital that is 58 times that in the US So capital does not ow But there is another simple exercise that is informative lf capital is paid its marginal product then 04 FKg But this means that we can estimate the return to capital across countries by MPK a 1 where i indexes the country It is rather easy to get data on capital output ratios across country Before collecting it however we should also take into account the fact that output will be sold at H in country i and that the cost of capital goods is P1 Then we should examine the true holding return M PK de ned by P39 P Y JWPIC l4PIQ l 2 1 PI PIQKgti Investment Ratios Spring 2004 Rather than measuring the capital output ratio at world prices we adjust each for domestic price levels and distortions This will be important as this ratio will differ dramatically across countries Suppose we do this what do we nd From 1 we can see that much of the conundrum goes away Without the domestic price adjustment we can already explain a lot Take 1ndia With a 13 the ratio of Ig 226 But using 1 we nd MPKIndm 055 compared with 037 for the US Essentially 1ndia uses less capital per unit of output than the US and this shows up in the ratio 1t is due to lower productivity of course When we do the calculation according to 2 then we have MPKIndm 032 compared with 046 for the US This shows up similarly for most countries The point being that distortions in domestic prices make the returns to capital across countries look normal3 Another way to look at this result is with regard to Argentina With the Lucas calculation its return to capital is 11 times that of the US At international prices it is about 20 higher than the US 043 versus 037 But correcting for distortions it is about 30 lower than in the US 035 versus 046 Hence correcting for the distortions we see why capital does not ow to Argentina very easily4 These price distortions suggest that at domestic prices poor countries are not investing so much less than rich ones The problem is that they get less investment for a unit of expenditure At domestic prices the correlation goes away Thus while the correlation between y and is 050 when measured at PPP the correlation between iy at domestic prices and y at PPP is only 005 1t is well known that investment rate differenHSL39502bmpe when measured at a common set of prices while very small when measured at domestic prices Evidently the domestic price of investment goods is high relative to consumption in poorer countries Why 1s this due to tariffs and taxes or is it more fundamental 3This should not be surprising since capitaleoutput ratios do not vary much across countries In the Solow model capital labor ratios differ in different steady states but capital output ratios vary less 7 one of Kaldor s stylized facts 4This may be the place to point out the importance of studying Argentina and Latin America for devele opment In 1913 Argentina s GDP pericapita was 80 of the OECD average By 1987 it was 32 This is quite dramatic and explaining why a country diverges must be as important as why it converges Maw 30 Manpold pu mw pewmmsa emu than pass22293 mm W m mm M aux mug Suuds swung muqu Investment Ratios Spring 2004 Hsieh and Klenow pursue this and show that investment goods are no more expensive in poor than rich prices The high relative price of capital is primarily driven by lower US PUS consumption goods prices It is not Fm that differs so much but LPMQW I O The argument is that in poor countries investment sectors have low productivity relative to their consumption sectors This is a corollary to the Balassa Samuelson hypothesis Tradable investment goods but not all tradable consumption goods Nontradable consumption goods in poor countries are cheaper than tradable investment goods That is what causes the relative price difference But what causes this productivity difference 2 Model The Hsieh Klenow model has two sectors and two tax rates a nontradable consumption sector a tradable investment sector a tax rate on importing investment goods 717 and a tax rate on capital income TKjO Otherwise it is a standard neoclassical growth model Each of Lj workers in inelastically supply one unit of labor per period They choose consumption to maximize gt0 Cl 2 t l f i 3 t0 a subject to Kjt1 1 5V9 1327 4 Pomoji T 13172111 wilt T lei T TKj Bit T 6P1jzl K13 T Tiquot 5 and Rjt1 7K1 73 51 719 1317 Or 6 7 6 V 3 Wit 7K7 p1 6 1 7 7K 7 where R is the rental price of capital and T are transfers from the government and are rebated tax collections Expression 6 is just an expression for the rental cost of capital Rest is standard Investment Ratios Spring 2004 Key Assumption Consumption goods cannot be traded internationally but investment goods are tradable The pre tax world price of investment is taken as given PIW Then PIj TTIJ39PIW39 In each country rms rent capital and hire labor in competitive spot markets They sell output in competitive markets to maximize current pro ts given by HG E P07 Cj 7 ijcj 7 PLqu 8 and H1 2 PIWIj i ijIj i Pth because investment goods are tradable This can be rewritten as H1 2 PIjIj i TIjPIWIj i ijIj i RjKIj 9 Production technologies in the two sectors are c ACnglecf 10 and I AIngL 1 11 where A17 and A07 are productivity indexes It is assumed that 04 is the same across countries and across sectors within countries The FOC s that come from this problem allow us to write K 071 31 aPIW A17 1 12 Lj and5 P Cy A 1 P 1W A07 5Why are the capital labor ratios equal From the FOC for labor we have w 1 7 0413914016 1 7 aP1wA1kjquot c Q71 sci Q 153 Q f where the last equality comes from the FOC wrt to capital Hence7 k1 kg 6 1 a 6 Investment Ratios Spring 2004 which implies PC A 7 7 13 P17 A0jl 717 Expression 12 equates the rental price of capital to the marginal product Expression 13 says that the relative price of consumption goods is inversely related to relative TFP in the two sectors and is decreasing in the tax rate on importing goods These are the two key factors The important thing is to separate out the two factors To make this tractable they assume that some basic parameters 6 039 and 6 are the same across countries Moreover sectoral TFP s grow at the constant rate gA across sectors and across countries6 The parameter values that can vary across countries are 719717141 and A0 Thus TFP grows at similar rates but they can differ across sectors or countries at a point in time Variation in the parameters 719717141 and A07 generate cross country variations in steady state levels of the investment rate at domestic prices the domestic price of investment and the domestic price of consumption They also yield different levels of PPP levels of y at a point in time across countries Notice that because of 7 and the assumption that consumption is nontradable there are no opportunities for international commodity arbitrage There are also no incentives for international capital mobility because capital is taxed where it is located After tax after depreciation real interest rates are the same in all countries and equal to 77 W this follows from the consumption Euler equation 7 it is the Keynes Ramsey rule 7 plus the 1 14 steady state assumption With no capital ows we have savings equal to investment within countries The investment rate at international prices can be written using 10 and 11 as L 471717 PfWAIj k1 739 a 1 prpA1k1aLL E Pamela 7 6This latter assumption is not critical Investment Ratios Spring 2004 which can be rewritten as PfPPAI imp LIV 7 Li LIV 15 PfWAIjL j Pg ch 1 7 because the capital labor ratios in the two sectors are equal The key implication of this equa tion is that low TFP in investment relative to that in consumption can cause the investment rate at PPP to be lower Now consider what happens if A1 falls holding AC xed From 15 it is clear that invest ment rate falls This means that the fall in aggregate TFP will be greater than just the direct effect via its size7 The reason is that capital accumulation is also affected This is impor tant Not only do poor countries have lower TFP than rich ones but they have especially low 41 s Their low sectoral TFP s contribute to their low aggregate TFP and their low 2 ratios contribute to their low physical capital intensity in PPP terms Figuring out why A1 is so low is very important 3 CrossCountry Evidence If the quotinvestment barriersquot hypothesis is true then investment prices should be cheaper in rich countries So if the prices of machinery and equipment are converted to dollar prices at o icial exchange rates or using black market premia then there should be a negative relationship with PPP income But this does not appear in the data see gure for o icial exchange rates Suppose that one regresses the price of investment goods machinery or xed investment on the log of ya either using o icial exchange rates or black market rates to convert in vestment prices If the quotinvestment barriersquot hypothesis is true then the coe icient on yppp should be negative But in the data it is insigni cant and the R2 is very low In some case investment prices appear more expensive in rich countries 7The direct effect follows because we can express economyiwide TFP as L 7 L L TFPJ 13ch J Lj 17 prpAIj L9 7 Investment Ratios Spring 2004 The high PPP rates of investment in rich countries is due not to low prices of investment but high relative prices of consumption This is consistent with B S nontradables are relatively cheap in poor countries But why are tradable consumer goods cheaper in poor countries Perhaps it is distribution costs But why is investment relatively ine icient in poor countries 0 nancial underdevelopment leads to bad project selection 0 public investment is relatively higher and this is ine icient relative to private Whatever the explanation and more later this implies that poor countries do not appear to lack investment e ort 7 they lack investment e icieney8 Of course this should imply that developing countries should import investment goods In the model there are no tradable consumer goods to export but surely in practice developing countries import a large share of machinery 4 Digression Government Production of Investment Schmitz JME 2001 considers the impact of government production of investment goods If the government is less e icient at producing investment goods this will have a productivity impact on the economy He uses a similar framework He notes that there is a direct and indirect effect 0 direct e eet is lower output and labor productivity in sector I o indirect e eet is that on the rest of the economy through lower capital per worker 8To recap poor countries do not exhibit particularly low investment rates at domestic prices Nor do they exhibit high investment goods prices Instead they exhibit low consumption prices When consumption is valued at common PPP prices in all countries the investment rates in poor countries are lower than in rich countries Poor countries do not appear to suffer from lowisavings traps brought on by high discount rates or subsistence consumption needs If they did we would expect to see much lower domesticiprice investment rates in poor countries Nor do they appear to heavily tax the returns to capital If they did we would expect to see low domesticiprice investment rates in poor countries Finally poor countries do not appear to impose high taxes and tariffs on producing and importing investment goods If they did we would expect to see high investment good prices in poor countries Poor countries do not appear to lack investment effort but rather investment ef ciency Investment Ratios Spring 2004 Suppose we are in a steady state then from earlier we know that R Lyn11kg 1 aPCACkf l 16 we also know that relative prices satisfy where 1 have set 739 1 Then the steady state capital labor ratio satis es p W 1410451 17 Now suppose that the government produces all investment goods and that TFP is now given by MA p lt1 Then 1 A P E W 1410451 18 so that the effect of this ownership policy is E 1 To 19 k M1 Just to have an idea suppose that 04 13 and that M 12 Then E 035 Steady state capital stocks are 35 of what they would be without this policy This is the direct effect Notice that this policy will also change the relative price of investment goods This should not surprise given Hsieh Klenow Before the policy we had now g 41 which implies that the relative price of investment goods doubles What happens to aggregate TFP Let yZPPP be detrended output under policy i 17 2 where the latter is the policy of government ownership Then it is straightforward to show that PPP a y i i k in lt1 7 n m 20 341 1 where n is the share of the labor force that works in the investment sector in the steady state Using 19 we can write ygppeminw 1 aww 1 nyP i I Fm M i quot1 PW M L 17 10 Investment Ratios Spring 2004 Now suppose that 80 of the labor force is in consumption and 20 in the investment sector And suppose that we continue to let M 05 Then we obtain 15 08 020lt05 050395 Dynamo5 636 which means that the policy of government production of investment would reduce aggregate productivity to 64 of its potential level Of course any of these calculations depend on the value of M Schmitz cites independent studies for Turkey and Egypt which show that stateowned capital goods rms are half as productive as privateowned ones These may seem large but it is important to note that we are not talking about natural monopoly type industries in this case These differences perhaps then re ect some of the costs of regulations that the stateowned rms operate under that the private ones do not Of course there may also be some selection issues that arise from the de nition of industries too broad categories for example More studies needed Notice that if you take into account the fact that government ownership is not 100 then you face some modelling questions How do private and state rms coexist if the latter are less e icient Either they produce different goods which is not too inviting since we would then need to know how substitutable they are Or you could assume that taxes and subsidies are used to allow coexistence It may also be the case that the government mandates the share of the sector that will be stateowned 402 General issues 1 Are government owned rms inherently less productive It would seem so We know why for planned economies Some of these factors however do not apply to developing economies relative prices are market determined there is no central plan no seller s market The causes in this case are primarily organizational 7 absence of free entry and selection and perhaps rent seeking that ensues Could also be extra corruption 0 Indeed one might think that the reason why governments want investment goods sectors 11 Investment Ratios Spring 2004 to be stateowned is that it makes corruption easier to facilitate It is harder to know the price of capital goods so kickbacks are easier to conceal The more frontier the technology the harder to judge the price so bureaucrats may want to encourage imports of such goods to get kickbacks 2 Why is the problem of government ownership more important in developing economies It could partly be a sectoral priorities issue Heavy industry is more important Command ing heights Although government shares of GDP are similar across countries government ownership of manufacturing differs greatly And in countries where there is data this seems concentrated in investment goods sectors Rent seeking opportunities must be a part of this Also they may need protection to survive competition from imports from more developed economies Legacies of import substitution 4 Speci c HiK issues Sum up HampK can explain 0 The cross sectional patterns of correlations particularly for later years 0 The increasing gap between the two correlations over time For this the model should be extended to feature higher growth of 141140 in richer countries 0 Still in need of explanation is the declining correlation of investment rates in domestic prices and income over time Conclusions from this exercise 0 Poor countries have low levels of physical capital The paper claims that this is NOT because they have sacri ced little consumption or invested little in domestic There is some truth to this Poor countries did not save necessarily less in the 90 s in domestic However current levels of capital are the result of decades 12 Investment Ratios Spring 2004 of accumulation and it seems that a few decades ago poor countries were indeed sacri cing less consumption 0 So it can still be true that the low levels of capital today are the result of little sacri ce in the past We need ner development accounting Some other implications The benchmark model has one tradable 1nvestment goods are tradable Consumption goods are not tradable Hence no good is traded in equilibrium There is no motive for trade because there is only one tradable o What happens when trade is allowed for 1e when the poor can produce tradable consumption goods with a comparative advantage 0 With trade the prediction that Car Mippp Y gt 0 weakens ie this correlation is lower with than without trade This is because the share of tradables in consumption declines with income 0 Since in the data Corr 1R in PPP prices Ygt0 is robust this suggests that in practice trade between developed and developing countries is negligible 0 Why is trade so low Barriers to trade in DC Protection of primary sectors Productivity of tradables too low in LDC o Suggests another test Corr 1R in PPP prices Y should be higher for countries that trade little with DC9 1s P1 equal across countries While measured P1 can be equal effective P1 might differ This could occur due to higher risk in Developing Countries eg risk of expropriation is higher 91f you split the sample into two groups Low and High Trade the CorriPPPY is higher for lowetrade countries opencltmedian 7 CorriPPPY 071 if OpennessltMedian 1996 CorriPPPY 016 if OpennessgtMedian 1996 Good for HampKl But do check other years 13 Investment Ratios Spring 2004 o This higher risk constraints the technology choice set leading countries to adopt less e icient technologies This could be behind the choice of less productive technologies Why should productivity in nontradables rise slower than productivity in tradables Two possible explanations are 0 tradables have greater inherent capacity for productivity improvement because more mechanized and capital intensive o tradable goods have larger scale due to larger markets so the return to innovations may be greater Why is the production of investment goods so ine icient in poorer countries One expla nation is government production Another may relate to scale and markets 5 Conclusion Poor countries have low levels of physical capital 1n the 90 s they did not invest less than the rich in domestic But they seemed to have invested less in the 60 s 80 s So to some extent current low levels of capital might still be the result of low sacri ce of consumption early on References De Long J Bradford and Lawrence H Summers quot How Strongly to Developing Economies Bene t from Equipment Investmentquot Journal of Monetary Economics 32 3 December 1993 395 416 14
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