The Impact of Budget Deficits, Public Debt and Education Expenditures on Economic Growth in Poland

Transcription

1 Michał onopczyński * The Impact of Buget eficits, Public ebt an ucation xpenitures on conomic Growth in Polan Abstract This paper investigates the relationship between economic growth in Polan an selecte elements of fiscal policy. The workhorse is the Mankiw-Romer-Weil moel augmente with selecte concepts from optimal fiscal policy literature. The government chooses the size of the eficit relative to GP an controls the structure of public ebt. It also ecies how much to invest in eucation, an how much to spen on public consumption. We prove that with constant values of parameters of fiscal policy, over time the economy converges to the balance growth path which is unique an globally asymptotically stable. aving calibrate the moel with statistical ata, we emonstrate that in the perio economic growth in Polan was riven primarily by rapi improvement in the level of human capital (at a rate of 5.4% per annum), an only seconarily ue to the accumulation of capital (2.7% annually). If recent trens in fiscal policy are continue, Polish economy will converge to the balance growth path with GP growing at 3.69%. This rate may, however, be booste, provie that fiscal policy is appropriately ajuste. or example, reucing buget eficit from recent average value of 4.3% of GP own to 2.3% woul spee up economic growth by approximately 0.2 percentage points. We also analyze the effects of changes in the financing structure of public ebt. inally, we present several scenarios of increasing public an private spening on eucation. JL classification coes: 13, 62, 43, 6, 52. eywors: optimal fiscal policy, economic growth, human capital, public eficit, government ebt. Introuction In onopczyński (2014) we have evelope a simple exogenous growth moel intene to investigate the long-run effects of certain moifications in fiscal policy. In particular, our moel was capable of simulating the long-run effects of changes in tax rates as well as * orresponence concerning this article shoul be aresse to: Michał onopczyński, Poznań University of conomics, al. Niepoległości 10, , Polan; michal.konopczynski@ue.poznan.pl. 1

2 ajustments in private an public spening on eucation. ollowing stanar approach in the theoretical literature see e.g. Lee & Goron (2005), hont & eylen (2009), an Turnovsky (2009) we have assume therein that the government maintains a balance buget in each perio. This assumption is theoretically justifie by Ricarian equivalence, at least in case of close economies see, for example, lmenorf & Mankiw (1998). owever, from an empirical point of view, it is obviously unrealistic. Therefore, the main purpose of this paper is to augment our previous moel by allowing the government to run eficit finance by omestic as well as foreign leners. The moifie moel allows for simulating the long-run effects of changes in the level of buget eficit (in relation to GP) as well as the structure of financing of public ebt. Last but not least, we also analyze growth effects of increase investment in eucation. The literature on long-run (growth) implications of public eficit an ebt is abunant. onopczyński (2015) provies etaile overview. Theoretical literature is almost uniformly base on enogenous growth moels, with all its strengths an weaknesses. To the contrary, our analysis is eliberately base on exogenous growth theory, which ates back to the nineties. There are quite a few arguments in favor of such an approach they have alreay been expose in onopczyński (2014). In short, we think that entral an astern uropean countries (incluing Polan) over the last 2-3 ecaes have experience so many eep, structural changes, that it woul be unjustifie to apply strong assumptions of enogenous growth theory. In particular, in our view it is not reasonable to assume that economic agents are continuously optimizing, smoothly ajusting their economic ecisions to evolving conitions, because these conitions change frequently, eeply, an often unexpectely. The expansion of the U in 2004 is probably the greatest of many eep, structural changes, which profounly affect economic conitions that consumers an businessmen face. or these reasons, our moel is eliberately constructe in much simpler way, with many elements taken irectly from the Mankiw-Romer-Weil (1992) growth moel. Therefore, human capital is a stock, which epreciates an requires investment just like other factors of prouction. urthermore, the rates of savings an investment are set exogenously. Mathematical rules escribing the public sector are mostly borrowe from the literature on the so-calle optimal fiscal policy; see e.g. Agenor (2007), Lee & Goron (2005), hont & eylen (2009), onopczyński (2015). There are five types of taxes: on capital, labor, human capital, interest on government bons hel by omestic resients, an consumption. Public expenitures are ivie into three broa categories: public consumption, eucation, an 2

3 financial transfers. The government chooses (fixes) the size of buget eficit relative to GP an controls the financing structure of public ebt. The paper is organize as follows. Section 1 presents the etails of the moel. Section 2 contains a qualitative sensitivity analysis. In section 3 the moel is calibrate for Polish economy over the perio Section 4 outlines the baseline scenario. In section 5 we search for the optimal level of buget eficit, whereas in section 6 we analyze the optimal financing structure of public ebt. Section 7 presents several scenarios of increase eucational expenitures by the government an by the private sector. In section 8 we search for the optimal structure of private investment. Summary synthesizes the main results an offers some further comments. Mathematical proofs are inclue in the appenix. 1. The moel The aggregate output of the country is escribe by the following prouction function: 1 a ( L), 0, 1 (1) where represents the stock of physical capital, represents the stock of human capital, an L is raw labor. ollowing Romer (1986) an Barro & Martin (2004) we assume positive externalities relate to learning-by-oing an spillover-effects, embee in the laboraugmenting technology inex function can be written as x L, where x const. 0. It follows that the prouction 1 A, (2) where A ax const 0. The labor supply in the country is growing exponentially: nt L L0e, where 0 0 L enotes the initial stock of labor (at t 0), whereas t 0 is a continuous time inex. eman for all factors of prouction results from the rational ecisions of firms maximizing profits in perfectly competitive markets. Let w an enote the real rental price of physical capital an human capital, respectively, an let w enote the real wage rate. In the profit maximizing equilibrium, all factors are pai their marginal proucts, i.e., MP w r, (3) w MP ( 1 ), (4) w MPL L L w, (5) 3

4 where represents the rate of epreciation of capital. Note that the variables w, w an w r represent gross rates (before taxation), i.e., the unit costs of labor, human capital an physical capital from the perspective of the representative firm. The public sector (the government) The government levies income an consumption taxes. Let L,, an enote the average tax rates on labor, human capital an physical capital, respectively. Taxes on labor an human capital are levie on gross wage rates, i.e., the government collects w L w an. To the contrary, the income tax on capital is levie on net capital income, efine as gross income minus a epreciation allowance, i.e. the tax bill is calculate as follows: ( w ) r. In aition, the interest on government bons hel by omestic resients is taxe with the rate equal to. The sum of all income taxes is expresse as where T wl w r r 1 L, (6) enotes the omestic ebt of the government. The consumption tax is equal to T 2, (7) where is the average tax rate on aggregate consumption. Total government revenue is T T 1 T 2. The real eficit of public sector J is the ifference between total government spening (incluing ebt servicing) an tax revenue, i.e. J G r T, (8) where G enotes government spening, an is the total public ebt. We assume that the buget eficit is fixe in relation to GP, i.e. J, (9) where const 0. Using (8), the bugetary rule (9) can be written as follows: G T r. (10) 4

5 Public ebt is accumulate accoring to the equation:. ertain part ( ) of bons is sol to foreign creitors, an the rest to omestic leners: with 0 1, (11) ( 1 ) (1 ), (12) where is the foreign ebt of the government. Obviously, at any moment of time,. Public expenitures inclue three components: G G G G, (13) T where G T enotes cash transfers to the private sector (mainly social transfers such as pensions, various benefits, etc.), G represents public spening on eucation, an G is public consumption (primarily health care, national efense, an public safety). By assumption, public consumption an eucation expenitures are a fixe share of GP: G, where 0 1. (14) G, where 0 1. (15) Obviously, 1. The equations (10) an (13) etermine the real size of the cash transfers: G G G G T r (. (16) T ) Accoring to this equation, the tax revenue augmente by the scheule buget eficit are use to service the public ebt, public consumption an eucation expenitures as planne by the government. Whatever remains is transferre to the private sector. The private sector On the one han, we assume that all factors of prouction are owne by omestic resients (to this en, the economy is close). On the other han the aggregate prouction function exhibits constant returns to scale. It follows that househols isposable income is equal to GP 5

6 6 net of taxes, plus the interest on government bons hel by omestic leners, plus transfers from the government. ertain fraction of that income is save, an the remainer is consume; hence the buget constraint of the private sector is expresse as follows: S G r T T T 2 1. (17) We assume a constant, exogenous rate of private savings: ) ( 2 1 T G r T T S. (18) Savings are use to either purchase government bons, or finance investment: I S. There are two types of investment: in physical an human capital, with a fixe share coefficient 1 0 : I )I 1 (, (19) I I, (20) rom (17), it follows that private consumption is equal to: S G r T T S T 2 1. (21) Notice that equations (18) an (21) are interconnecte because of (7). Accoring to (18), savings epen on consumption, an simultaneously, accoring to (21) consumption epens on savings. It is convenient to solve this system of equations. Substituting (16) into (18) an (21), an using (7), after simple transformation yiels: r 1 ) 1 ( (22) r S 1 (23) rom equations (12), (18), (19), (20), (23), an I S, it follows that: r I ) (1 1 ) 1 (. (24) r I ) (1 1, (25)

7 7 The accumulation of private capital an human capital is escribe as follows: I, 1 0, (26) I G, 1 0. (27) where an enote epreciation rates. These equations can easily be transforme to yiel the following growth rates: I ˆ, (28) I G ˆ, (29) Substituting (24), equation (28) can be transforme into the following form: r ) (1 1 ) (1 ˆ, (30) Similarly, using (15) an (25) in equation (29) yiels: r ) (1 1 ˆ, (31) inally, using (2), the growth rates (30) an (31) can be written as: r A 1 ) (1 1 ) (1 ˆ, (32) r A ) (1 1 ˆ. (33) or brevity, let us write qs. (32) an (33) in the following form: A 1 1 ) (1 ˆ, (34) A 1 ˆ, (35)

8 where 1 1 (1 ) r. (36) Note that it is necessary (though not sufficient) to assume that 1 0. Otherwise ˆ 0 or ˆ 0 (or even both), so that GP is shrinking to zero over time. This uninteresting (unwante) situation may happen if is very low (the private sector is saving too little), an/or if the government behaves irresponsibly. To be more precise, 1 may turn negative if, for example, the foreign-ebt-to-gp ratio is above some critical level (implying very high cost of servicing foreign ebt on the economy), or if the expression ( 1 ) is high enough, which means that the government is running very high eficit covere too extensively by omestic borrowing. Technically, the laws of motion (34) an (35) are similar to their counterparts (36) an (37) in onopczyński (2014). owever, augmenting the moel by aing public eficit an ebt has significantly complicate the ynamics of the moel. ining the balance-growth equilibrium in onopczyński (2014) was relatively simple it boile own to equating the right-han sies of equations (36) an (37) therein, an solving (numerically) the resulting nonlinear equation in one unknown (the ratio of ). Now it is more complicate, because the laws of motion inclue an aitional variable, the foreign-ebt-to-gp ratio, which evolves over time accoring to the following equation: ˆ ˆ ˆ. (37) ortunately, the following proposition can easily be prove. 8

9 Proposition 1 (proof in the Appenix) Over time, ˆ, regarless of whether ˆ is constant or changing over time. Intuitively speaking, it means that the foreign-ebt-to-gp ratio is continuously converging to the ratio of public eficit covere by foreign sources (as percentage of GP) an the rate of growth of GP, regarless of any changes (increase or ecrease) in the latter. This proposition leas to Proposition 2 (proof in the Appenix) In the long run, the economy converges towars the balance growth path (hereafter enote by overbar), with,, an growing at the same, constant rate (the balance growth rate, BGR). This balance growth equilibrium is unique an globally asymptotically stable. The steay-state foreign-ebt-to-gp ratio is equal to BGR const. 0 (38) The easiest way to fin the balance growth path is to equate the right-han sies of qs. (32) an (33), incorporating q. (38). This results in the following system of 2 equations in 2 unknowns, an : 1 ( 1 ) A1 A 1, (39) (1 ) A1 1 (40) where 1 is a function of substituting the obtaine value of given by q. (36). The BGR can then be calculate by into either (32) or (33). 9

10 Obviously, it is not possible to erive an explicit formula for the BGR as a function of the parameters of the moel. It can only be calculate numerically, after substituting some values for all parameters. Nevertheless, it is perfectly possible (an worthwhile) to perform a qualitative sensitivity analysis in orer to etermine the relationships between the parameters of the moel an the BGR. 2. Qualitative sensitivity analysis In this section, we investigate how changes in parameter values influence the BGR. The analysis is performe in 3 stages. irst, we investigate whether an increase in the value of a selecte parameter (,, etc.) increases or reuces the value of 1. Secon, using formulas (34) an (35), we investigate whether the graphs of functions ˆ ( / ) an ˆ ( / ) shift up or own. Thir, base on these observations, we conclue whether the intersection of these curves, which etermines the BGR (see Appenix, fig. A1), moves up or own. On the face of it, these stages are ientical as in the moel without public prouctive services see section 3 in onopczyński (2014). owever, stage 2 is far more complex than therein, because functions ˆ ( / ) an ˆ ( / ) epen on. In fact, this stage must be ecompose into 3 steps. irst, we investigate how the aforementione graphs shift uner an artificial assumption that the steay-state value of is not affecte. Secon, we investigate how the steay-state value of changes, an how it shifts the graphs of ˆ ( / ) an ˆ ( / ). Thir, we investigate the combine effects of these two shifts. As an example of this proceure, let us present in some etail the analysis of the effects of an increase in the eficit-to-gp rate. It s useful to follow all steps in figure 1, starting from the initial graphs of functions ˆ ( / ) an ˆ ( / ), labele ol ˆ an ol Ĥ. The intersection of these curves etermines the initial value of BGR labele ol BGR. 10

11 1 Note that (1 ), which may be negative, positive or equal to zero. Therefore, we must istinguish 3 cases: A. ( 1 ), B. ( 1 ),. ( 1 ). ig. 1. The effects of an increase in the rate of government eficit in case A. O for initial A N for initial irst, consier case A. Note that 1 (1 ) 0. It follows from qs. (34) an (35) that an increase in shifts both functions ˆ ( / ) an ˆ ( / ) own to their new positions, which in figure 1 are labele A ˆ for initial ; A Ĥ for initial, respectively. Therefore the BGR instantly falls. We may call it an immeiate effect. If the steay-state value of woul remain at this initial level, then the new BGR woul simply fall own to the level labele A BGR, an our analysis woul be complete. owever, will not remain at its initial level, as lower BGR couple with higher value of implicates higher value of, which follows irectly from q. (39). This, in turn, in accorance with equations (34) an (35) 11

12 shifts both functions ˆ ( / ) an ˆ ( / ) further ownwars to positions labele ˆ new an new Ĥ. We may call it the graual effect, because it is obviously sprea over time: lower GP rate of growth couple with higher eficit-to-gp ratio cause graual accumulation of public ebt, which graually (quarter after quarter) increases the buren of public ebt weighing on the economy, thus graually reucing both rates of growth, ˆ an Ĥ. Therefore it is clear, that in case A higher government eficit reuces the BGR. To provie an intuitive explanation of a negative relationship between an the BGR let us consier a stylize example. Recall that in this case ( 1 ), which means that the share of omestic leners in financing government eficit (an ultimately public ebt) is higher than their average rate of savings (out of their isposable income). Let ( 1 ) 60% an 30% (As we will see below, these parameters are similar in Polan over the last 2 ecaes or so). Imagine that the government ecies to increase its eficit by some specifie amount of money, say, 100. Thus it must borrow aitional funs from omestic an foreign leners. As ( 1 ) 60%, it borrows 60 from omestic leners (an 40 from foreigners). An increase in public eficit can be implemente with either a reuction in taxes, or an increase in financial transfers to the private sector G T, or an appropriate combination of both 1. Irrespective of the chosen metho, the 100 increase in public eficit results in an immeiate increase in private sector s isposable income equal to 100. This extra income is partly save, accoring to q. (18). As 30%, private savings increase by 30. owever, since 1 Strictly speaking, in our moel, it is an increase in financial transfers, accoring to q. (16). owever, in practice it is just one of 3 options. 12

13 ( 1 ) 60%, the private sector meanwhile purchases 60 worth of government bons 2, so that the net change in private savings is in fact negative an equal to minus 30. onsequently, private investment in both types of capital fall, reucing the GP rate of growth. (All of this are elements of what we call an immeiate effect; we will not elaborate on the graual effect, because it has been clarifie above.) Let us now consier case B, with 1 (1 ) 0. It follows from qs. (34) an (35) that an increase in shifts both functions ˆ ( / ) an ˆ ( / ) upwars to their new positions, which in figure 2 are labele A ˆ for initial ; A Ĥ for initial, respectively. Therefore, contrary to case A, the immeiate effect is positive: the BGR instantly raises. If the steay-state value of woul remain at this initial level, then the new BGR woul simply raise to the level labele A BGR, an our analysis woul be complete. owever, will not remain at its initial level, as higher BGR couple with higher value of implicates a ifferent value of, which follows irectly from q. (38). This, in turn, in accorance with qs. (34) an (35) shifts both functions ˆ ( / ) an ˆ ( / ) further. owever, without aitional assumptions, we cannot etermine the irection of this seconary effect we cannot be sure whether it is an upwar or ownwar shift. Moreover, we cannot exclue a possibility of a negative graual effect being big enough to finally offset (or even more than offset) positive immeiate effect. To see why, let us consier the bounary 2 We assume that the private sector (somewhat passively) purchases any amount of bons that the government supplies. In practice, it coul be realistic in such countries, where the public sector is relatively large, an the government has significant share in the banking sector an/or irect control over some large state-owne companies. We claim that Polan has recently been such a case, an in fact is recently moving more an more towars such a situation. 13

14 case, where ( 1 ), so that 1 (1 ) 0. Obviously, in this case there is no immeiate effect: both curves ˆ ( / ) an ˆ ( / ) initially remain unchange, so that initially the BGR is not affecte. owever, there is a negative seconary effect, because higher value of raises the steay-state value of. This, in turn, in accorance with equations (34) an (35) shifts both functions ˆ ( / ) an ˆ ( / ) ownwars. This graual effect is sprea over time: falling GP rate of growth couple with higher eficit-to- GP ratio cause graual accumulation of public ebt, which graually increases the buren of public ebt, thus graually reucing both rates of growth, ˆ an Ĥ. ig. 2. The effects of an increase in the rate of government eficit in case B. for initial A N O for initial Therefore it is clear, that in case B, negative graual effect may well be big enough (in absolute terms) to more than offset the initial positive effect, so that the BGR may finally be lower than its initial value, i.e. new ol BGR BGR. This will happen, if 1 ) (, but the ifference is small enough. 14

15 The effects of an increase in all other parameters can be trace own in a similar way. In some cases, the initial change (increase/ecrease) in BGR is partially, entirely, or even more than entirely offset by the seconary effect: graual change (ecrease/increase) in. The results are summarize in table 1. Table 1. Qualitative sensitivity analysis L 1 = = = = =?? graph of ˆ ( / ) graph of ˆ ( / ) = = = =?? = = = =??? BGR = = = =???? = = = =???? = = = =????? Some conclusions are intuitively clear, but others eserve explanation. irst, let us note, that all tax rates in our moel are neutral, which is a common result in theoretical literature, an is a irect consequence of strict fiscal rules embee in the moel. Recall that two out of three components of public expenitures are fixe in relation to GP, just like the size of buget eficit. Therefore, any change in tax revenue translates into an ientical (equal in size) change in the thir component of public spening, which happens to be transfers to the private sector. Put simply, any aitional taxes impose on private sector immeiately return to that sector as financial transfers. Thus, the isposable income of private sector is immune to any changes in tax rates, which implies that the equilibrium (balance growth path) is also entirely insensitive to changes in tax rates. owever, these are the only parameters of the moel that are neutral: all remaining parameters o influence the BGR. 15

16 or example, unsurprisingly, increasing the rate of private savings spees up the accumulation of both types of capital (technically speaking, it shift both curves ˆ ( / ) an ˆ ( / ) upwars), thus raising the BGR. To the contrary, raising, i.e. increasing public consumption in relation to GP, reuces the BGR. This is also the result of applie fiscal rules: for a given level of tax revenue an public spening on eucation (both in relation to GP), an increase in requires an appropriate reuction in public transfers to the private sector, in orer to keep the level of buget eficit unchange (as percentage of GP). Thus, an increase in public consumption has a etrimental effect on the isposable income of private sector, an this in turn leas to lower level of private investment in both prouctive capital an eucation. Remarkably, the relationship between an the BGR is ambiguous. Recall that represents the size of public spening on eucation in relation to GP. One might expect that raising shoul lea to higher rate of growth of human capital, an therefore higher BGR. This is, however, not always true. or clarity of explanation, let us now focus on the immeiate effect (i.e. neglect graual effect). 1 On the one han, 0, so it follows from q. (34) that an increase in shifts the curve ˆ ( / ) ownwars. It follows irectly from strict bugetary rules that the government must obey: given the fixe eficit-to-gp ratio, fixe tax revenue an fixe public consumption, raising automatically reuces cash transfers G T to the private sector, thus reucing its isposable income an savings, which reuces both types of private investment. 16

17 ( 1 ) 1 On the other han,, which may be positive, negative or zero epening on the factual values of parameters an. Thus, it follows from q. (35) that an increase in shifts ˆ ( / ) upwars, ownwars, or leaves it unchange. Therefore, an increase in raises the BGR, if the ˆ ( / ) curve not only shifts upwars, but it shifts strongly enough to offset the negative effect of the ownwar shift of the ˆ ( / ) curve. Note that it requires sufficiently low value of couple with sufficiently low value of. This conclusion has clear-cut, intuitive interpretation: low values of an mean that the private sector saves little an, moreover, spens most of these small savings on prouctive capital rather than eucation. In such a case an increase in public spening on eucation is beneficial: although it slightly reuces private savings an investment in prouctive capital (ue to strict fiscal rules explaine above), it boosts the rate of growth of human capital significantly, so that the net effect is positive: the GP grows faster. Let us now turn to, which represents the share of private savings investe in eucation. Accoringly, raising increases the rate of human capital accumulation an reuces the rate of growth of physical capital. Thus, the graph of ˆ ( / ) shifts up, whereas the graph of ˆ ( / ) shifts own. The intersection of these curves unambiguously moves to the left, but it is unclear whether it moves up or own. Therefore, a higher value of reuces the balance growth ratio of / there is more human capital per each unit of physical capital. Nonetheless, the relationship between an the BGR is ambiguous. The relationship between an BGR is also ambiguous. To be more precise, it is positive for sufficiently low levels of r, but negative if r excees certain critical value. To see why, 17

18 1 let us first consier a trivial case, where r 0. It follows from (35) that 0, so that an increase in shifts both functions ˆ ( / ) an ˆ ( / ) up, unambiguously rising the BGR. An intuition behin this result is simple: if the government can borrow abroa for free (at zero cost), it makes perfect sense to finance the entire eficit (an ultimately public ebt) from foreign sources. Such policy leaves more money in the hans of omestic private sector, facilitating higher level of savings an investment, which is beneficial for economic growth. Let us now turn to more realistic situation, with r 0. In that case we shoul use the same 3-stages proceure as we applie above to. To keep our analysis more concise (an avoi repeating some explanations an graphs), we will, however, not present all etails. Instea, we will focus on intuition. Note that an increase in prouces a positive immeiate effect: regarless of the value of r, an increase in instantaneously raises the value of, 1 shifting both curves ˆ ( / ) an ˆ ( / ) upwars, which boosts economic growth. Over time, however, bigger share of foreign lening in public ebt results in steaily climbing value of, an this in turn graually shifts both curves ˆ ( / ) an ˆ ( / ) ownwars. Whether this negative, graual effect will be big enough to eventually offset the initial, positive effects epens on the value of r : for sufficiently high value of r, the buren of rising foreign ebt will over time become so substantial, that the GP rate of growth will ultimately ecline below the initial level. Intuitively, this conclusion is perfectly comprehenible: if the cost of borrowing by the government excees certain critical level, the government shoul borrow omestically rather than abroa it s better to pay high interest to omestic leners (the funs will remain in the country as investment or consumption) rather than foreigners. owever, if the cost of borrowing is sufficiently low, this avice turns upsie own: it s better to finance public ebt by borrowing abroa rather than omestically: in such a case, aitional funs borrowe 18

19 abroa an (in certain part) investe omestically yiel positive effects (which may be measure by the rate of return on capital an eucation) which outweigh the cost of borrowing abroa. These qualitative results, though interesting per se, only enhance our esire for quantitative results. Moreover, as the BGR cannot be etermine analytically, it is not possible to etermine how strongly changes in the values of parameters influence the BGR. In other wors, we alreay know the irection of the effect, but we know nothing of the size of the effect. Answering these questions requires calibrating the moel an performing numerical analyses. In what follows, we calibrate the moel for Polan an numerically analyze optimal fiscal policy, as well as optimal private sector parameters. The calibration is base on macroeconomic ata for Polan for the perio , publishe by the urostat, IM, O, an the iel Institute for the Worl conomy. Public sector 3. Moel calibration for Polan The eficit of the public sector in Polan calculate in accorance with urostat methoology is presente in fig. 3. It fluctuate willy between 2% an 7.3%, with the minimum shortly before, an the maximum uring the Great Recession. On average, bugetary eficit was equal to 4.3% of GP, thus we set 4.3%. ig. 3. General government eficit in Polan (% of GP) 19

20 Source: urostat. Table 2 presents the level an structure of public ebt in Polan. The best statistical measure of net foreign ebt of the government is the (inverse of) net international investment position (NIIP) of the public sector. Subtracting it from total public ebt yiels omestic ebt of the government. Table 2. Public ebt in Polan. ear Total public NIIP of the public omestic ebt of ebt sector the government ,5-17,7 18, ,3-14,6 22, ,8-15,4 26, ,6-17,7 28, ,0-19,7 25, ,4-19,3 27, ,9-18,1 28, ,2-16,4 27, ,3-12,5 33, ,4-18,4 31, ,1-22,0 31, ,1-23,1 31, ,7-28,9 24, ,7-27,7 28, ,2-28,5 21, ,1-28,4 22, ,1-27,5 26,6 Source: National Bank of Polan (NBP) an own calculations. The share of foreign ebt in total public ebt (fig. 4) fluctuate between roughly 35% an 55%, with a sharp but temporary rop in 2008 (ue to rapi fluctuations in the value of Polish zloty inuce by financial crisis aroun the worl). or our calculations we will aopt the average value over this perio, which is equal to Likewise, the average value of public ebt over the same perio will serve as the initial value (enowment), i.e. we set ( t 0) 47.8%. The real rate of return on 10-year government bons in Polan over the perio was, on average, equal to 3.3% (source: NBP), thus we will assume that r 3.30%. 20

21 ig. 4. The share of foreign ebt in total public ebt ( ). 60% 50% 40% 30% 20% 10% 0% Source: National Bank of Polan (NBP) an own calculations. Public expenitures on eucation in Polan uring the perio (the latest available ata) were on average equal to 5.62% of GP (source: urostat); hence base on formula (15), we set 5.6%. The value of is calibrate on the basis of statistics regaring final consumption expeniture of general government, which over the perio amounte to 18.4% of the GP (an was very stable). This statistical aggregate inclues, in particular, public spening on eucation, which in our moel is single out as a separate component of public expenitures. Subtracting 5.6% yiels 12.8%. Private sector Technological parameters The elasticities of the prouction function (1) have been estimate in many papers, e.g., Mankiw, Romer & Weil (1992), Manuelli & Seshari (2005). Stuies focusing on Polan inclue ichy (2008) an Próchniak (2013). The estimate values are typically close to 1/3; hence we set: As we argue in onopczyński (2014), the rate of physical capital epreciation is ifficult to estimate, ue to rapi economic transformation which resulte in huge amount of obsolete machinery, infrastructure, etc. inherite from the centrally planne economy. In various research papers regaring O countries, physical 21

22 capital epreciation varies from approximately 3.5% to 7%. As the focus of our analysis is on the long run, we set the epreciation rate at a rather low level of 4%, which is similar to Nehru & hareshwar (1993). The rate of human capital epreciation has been estimate by Manuelli an Seshari (2005), Arrazola an e evia (2004) an others. ollowing these authors, we set 1.5%. Next, we must assess the real rate of return on capital (r). rom (3), it follows that r. The ratio of is very ifficult to estimate for Polan we have expose major problems in onopczyński (2014). Most importantly, the ata available for Polan only reflect a fraction of all prouctive capital namely the gross value of fixe assets. Therefore in onopczyński (2014) we applie the average ratio from the entire sample of O countries in iel atabase, i.e., we set 1 3. Substituting this value into (3) yiels the real rate of return on private capital equal to r %. This outcome is very close to most long-run empirical estimates for O countries. or example, ampbell, iamon & Shoven (2001) report that the average real rate of return on stocks in the U.S. over the perio was 7%. In our opinion, analogous inicators for the Polish stock market are irrelevant, because Polish stock market is still too young an volatile, an presumably oes not reflect the long-run equilibrium. Social transfers an the rates of savings an investment The average rate of savings can be calibrate on the basis of qs. (17)-(20), which can be transforme into the following formula: S. Substituting (16) I I T r G T yiels: I I. (41) 1 r / 22

23 In orer to calibrate, we must first establish all ratios on the right-han sie. q. (12) implies that ( 1) ( ) 4.3% 2.43%. The initial ratio of foreign ebt to GP is / % 20.8%. Accoring to urostat, gross fixe capital formation in Polan in the perio was on average 20.2% of GP. Private spening on eucation in the perio (the latest available ata) was on average 0.65% of GP. Substituting all of these numbers into (41) yiels 20.2% 0.65% 2.43% 27.32% % 12.8% 5.6% 3.3% The share parameter can be calculate irectly from equation (20): I I I I I 0.65% 3.12%. Thus in Polan, a mere 3.1% of total 20.2% 0.65% private investment is investe in eucation. owever, private spening on eucation is probably unerestimate in official statistics urostat takes into account only school fees; materials such as textbooks an teaching equipment; transport to school (if organize by the school); meals (if provie by the school); boaring fees; an expeniture by employers on initial vocational training. All other private expenses relate to eucation are classifie as consumption, e.g., the cost of accommoation, travel, books, etc. Average tax rates urostat reports implicit tax rates on capital, labor an consumption. In Polan uring the perio (the latest available ata), these rates were on average equal to: 20.1%, 32.0%, an 19.4%, respectively. The average tax rate on interest income was 19,0%. L Note that the implicit tax rate on labor is efine as the Ratio of taxes an social security contributions on employe labor income to total compensation of employees. To the best of 23

24 our knowlege, there are no ata on the average tax rates on human capital. As we wrote in onopczyński (2014), some researchers suggests that for obvious reasons in countries with highly progressive taxes on personal income, tax rates on human capital must be higher than tax rates on (raw) labor. owever, in Polan, the size of tax wege on labor is nearly inepenent of the level of income, i.e., effective tax rates on wages are nearly linear. Thus, it is reasonable to assume that average tax rates on human capital an raw labor in Polan are ientical, i.e.,. L Recall that accoring to urostat, 32.0%. owever, if we set 32.0%, an L complete the rest of calibration as follows, the moel significantly overestimates the total revenue from income taxes (by approximately 4.3% of GP) 3. This problem arises because our concepts of human capital an raw labor are wier than urostat efinitions. In particular, urostat classifies taxes on income an social contributions of the self-employe as part of the capital income tax a etaile explanation can be foun in the methoological publication by urostat (2010), Annex B. owever, self-employe entrepreneurs efinitely correspon to our concept of human capital (as well as part of raw labor). Self-employment is very popular in Polan not only are there millions of small, family businesses, but very often iniviuals operate single-person firms an provie services for larger enterprises. Note that the tax rate on capital income publishe by urostat is much lower (20.1%) than the tax rate on labor (32.0%). Therefore, in our moel, the tax rate on human capital an labor shoul be somewhere between these two numbers. As there are no aitional statistics, we calibrate both rates at such a level, for which the moel yiels a total share of taxes in GP that is consistent with statistics (33.5%, see above). In so oing, we obtain 25.55% i.e., rates that are roughly 20% lower than those reporte by urostat. L L 3 In the perio total receipts from taxes an social contributions to GP amounte to 33.5% (an this ratio was very stable), whereas consumption taxes were equal to 11.9% of GP. Thus, the ratio of income taxes to GP was equal to 21.6%. 24

25 inal steps The next step in the calibration is computing the initial value of 1 0 from q. (36). Substituting all calibrate parameters into q. (36) yiels: nowing these values, an using formula (30), we compute the average capital growth rate uring the perio : ˆ (1 ) 2.73%. 1 The average GP growth rate in Polan uring the perio was 3.64%. nowing this, we can estimate the human capital growth rate, on the basis of equation (2), ˆ ˆ which implies that ˆ ( ) 3.64% % 5.45% (1 ) 1 3. These results imply that in the perio , economic growth in Polan was primarily riven by rapi growth in the stock of human capital, an only seconarily by the accumulation of prouctive capital. An impressive increase in human capital in Polan is a well-known stylize fact confirme by a sharp increase in the number of stuents, Phs, etc. or simulations it is necessary to set the value of the parameter A. irst, from equation ˆ (31), we calculate the proportion As 1 3, we get Transforming q. (2) an substituting the above ratios yiels A To perform the simulations, we shoul also assume certain initial (enowment) values of, an L. Two of these values ( an L) can be set completely freely, provie that we confine our interest to the rates of growth an relationships (the proportions) among variables. Therefore, we set L ( 0) 1 an ( 0) 300. This particular choice is convenient, as the initial level of GP is then equal to 100, so that 25

26 the initial values of all the other variables are ientical to their percentage shares of GP. Given the ratio , it follows that ( 0) In summary, we have the following base set of parameters an enowments: A , 1 3, 1 3, 4.0%, 1.5%, 27.32%, 3.12%, 0.435, 5.60%, 12.8%, 20.1%, 19.4%, 19%, 25.55%, (42) L ( 0) 1, (0) 300, (0) 89.88, (0) L 4. The baseline scenario Obviously, the baseline scenario with the set of parameters (42) reprouces actual statistics on the Polish economy uring the perio , in particular it reprouces factual (average) ratios of the following variables to GP:, I, I, T 1, T 2, G, G, as well as the (average) rate of GP growth. The rates of growth for t 0 generate by the moel in the baseline scenario are equal to ˆ 3.64%, ˆ 2.73%, ˆ 5.45%. These rates are not ientical, which implies that Polish economy is not yet on the balance growth path. Using the proceure escribe at the en of section 2, we can numerically obtain the BGR in the baseline scenario, which is equal to 3.69% marginally higher than the average growth rate uring the perio The process of convergence towars the balance growth path is presente in figure 5, which illustrates the trajectories of several growth rates in the baseline scenario. 26

27 5,5% ig. 5. Baseline scenario: convergence to the balance growth path 5,0% 4,5% rate of growth of rate of growth of rate of growth of 4,0% 3,5% 3,0% 2,5% Although the baseline scenario looks rather benign in terms of the BGR, note that the level of public ebt in this scenario rises to the angerously high level, reaching as much as 116% of GP (see table 3). It seems that Polish government cannot continue running such a high level of buget eficit (equal to 4.3% of GP, on average). We are now reay to simulate the effects of changes in fiscal policy, incluing buget eficit, the way public ebt is finance, an eucation expenitures. 5. The level of buget eficit Let us first present the results of scenario A1 an A2, where the government reuces buget eficit by 1 or 2 pp. of GP. Thus, in scenario A1 3.3%, whereas in scenario A2 2.3% (from t 0 onwars). Table 3 presents structural characteristics of new balance growth paths in both scenarios. 27

28 Table 3. Permanent reuction in buget eficit equal to 1 or 2 pp of GP. the BGR an structural inicators (%) baseline scenario 4.3% Scenario A1 3.3% Scenario A2 2.3% the BGR (the cumulate effect after 30 years= +2.3% of GP) 3.87 (the cumulate effect after 30 years= +4.6% of GP) / T / S / I / G / G / G / T I / / / The baseline scenario clearly inicates that Polan cannot affor to maintain buget eficit equal to 4.3% of GP, because over time the ebt-to-gp ratio woul more than ouble an reach almost 117%. Thus the baseline scenario is unacceptable from the point of view of Polish constitution, which sets the 60% ceiling on public ebt. Moreover, continuing current unbalance fiscal policy is simply harmful for economic growth, as both alternative scenarios prove. In both scenarios the GP grows faster (along the balance growth path) than in the baseline scenario: reucing the size of buget eficit by 1 pp. of GP rises the BGR by approximately 0.1 pp. It seems to be negligible, but remember that economic effects are accumulate exponentially over time. To better visualize these long-term (welfare) effects, table 3 inclues numbers inicating by how many percent GP excees baseline GP after 30 years (in table 2, numbers in parentheses). These inicators are calculate as follows: 28

29 ( t 30) in selecte scenario gain after 30 years 1. ( t 30) in the baselinescenario Let us now focus on scenario A2. Note that reucing buget eficit to 2.3% of GP woul keep the ebt-to-gp ratio within the constitutional constraints: over time it shoul stabilize at 59.4%. After 30 years, GP woul be 4.6% higher than uner the baseline scenario, which is not negligible at all. A precise (mathematical) as well as an intuitive (stylize) explanation of this fact has alreay been presente in section 2. Recall that we ha to istinguish 3 cases, an statistical ata implicates that Polan falls into case A, as (1 ) %. As we explaine in section 2, a reuction in (from t 0 onwars) prouces the immeiate effect (raising the GP rate of growth instantly) as well as the graual effect, which is slowly (year after year) raising the GP rate of growth further. Both effects are clearly visible in ig. 6, which contains the trajectories of rates of growth in scenario A2. ig. 6. Scenario A2 in comparison with the baseline scenario Scenario A2 entails some noteworthy structural changes. A permanent reuction of buget eficit by 2 pp of GP in the long run leas to approximately twice smaller cost of servicing public ebt, which results in significantly lower overall tax buren (it falls from 33.9% to 29

30 33.5% of GP). In the meantime, however, in orer to keep public spening on eucation an public consumption at the same level as before (5.6% an 12.8% of GP, respectively), the government ecreases financial transfers to the private sector by 0.5 pp of GP. Nonetheless, lower tax buren couple with lower borrowing nees of the public sector inuces a beneficial change in the structure of private spening: an increase in investment (from 19.9% to 20.7% of GP) couple with a slight rise in private expenitures on eucation. The accelerate accumulation of both physical an human capital shifts the economy towars a higher balance growth path. As a result, the BGR increases by 0.18 percentage points. inally, let us generalize these results further by assuming that the government can choose any value of (as long as it is not negative). ig. 7 presents the relationship between the BGR an. learly, the optimal level of eficit is zero, which means that in orer to maximize the GP rate of growth, Polish government shoul aim at balance buget (at least on average over the long run). ig. 7. The BGR as a function of. 4,2% 4,0% BGR 3,8% 3,6% 3,4% 3,2% 3,0% 0,0% 2,0% 4,0% 6,0% 8,0% 30

31 6. The optimal financing structure of public ebt Let us now return to the baseline scenario, an see how it epens on the value of the parameter. Recall that in the baseline scenario it is equal to 0.435, because recently 43.5% of public ebt was in the hans of foreign leners. We may rightly woner whether this is an optimal value. The soli-line curve on fig. 8 presents the relationship between the BGR an, assuming that all other parameters are taken from the baseline scenario. learly, the bigger the foreigners share of public ebt, the higher the GP rate of growth. This is the result of recent statistics: recall that over the perio the real rate of return on prouctive capital was equal to 7.11%, whereas the real rate of return on 10-year government bons in Polan was only 3.3%, which reflects a much lower (perceive) risk of lening to the government. The baseline scenario is a straightforwar extrapolation of these statistics, so obviously such a significant iscrepancy presents an opportunity (a specific type of arbitrage): for the country as a whole, it pays to borrow from abroa, an invest the procees in prouctive capital (as well as eucation). It may, however, easily change, if the cost of borrowing by the government raises significantly an/or the rate of return on prouctive capital ecreases. or example, as r raises, the relationship between the BGR an flattens out (see fig. 8), an for sufficiently high values of r it may even become negative. Thus, if the cost of borrowing by the government is sufficiently high (in our simulations exceeing circa 12.3%), our conclusion turns upsie own: it pays to reuce the foreigners share own to zero. In fact, in that case, the best long-run strategy is to reuce all of public ebt to zero, an run balance buget. 31

32 ig. 8. The relationships between the BGR an as r raises. 7. Scenarios of increasing public an private spening on eucation This section contains four scenarios of increase investment in eucation: B1. The government increases public spening on eucation by 1 pp of GP at the expense of public consumption. B2. The government increases public spening on eucation by 1 pp of GP at the expense of financial transfers to the private sector. 1. Private savings increase by 1 pp of GP (at the expense of consumption), with an unchange structure of investment expenitures (i.e., the same value of ). As a result, private investment in physical an human capital increase by a total of 1 pp of GP. 2. Private sector savings increase by 1 pp of GP (at the expense of consumption), however aitional savings are spent exclusively on eucation. (or this purpose, the value of has been appropriately ajuste). Put simply, private spening on eucation increases by 1 pp of GP at the expense of private consumption. Table 4 presents the results. 32

33 Table 4. Scenarios of increasing public an private spening on eucation B1 Increase in B2 The BGR an public Increase in structural spening on public inicators eucation by spening on 1 pp of GP eucation by (%) Baseline scenario 5.6% 12.8% 27.32% 3.12% 6.6% 11.8% the BGR GP effect after 30 years +10.2% 1 pp of GP 6.6% 3.97 GP effect after 30 years +8.1% 1 Increase in private savings by 1 pp of GP 28.47% 3.12% 3.91 GP effect after 30 years +6.8% 2 Increase in private spening on eucation by 1 pp of GP 28.47% 7.6% 4.03 GP effect after 30 years +10.1% / T / S / I / G / G / G / T I / / / / onclusions are similar to the results obtaine in onopczyński (2014). All three scenarios consierably outperform the baseline scenario. Importantly, scenarios B1 an 2 are better than B2 an 1, which means that the best option is to increase expenitures on eucation at the cost of public (scenario B1) or private (scenario 2) consumption. Both cases require a change in preferences of consumers: they must be willing to accept lower consumption (either public or private) toay (for some perio of time) in exchange for higher consumption in the future. Scenario B2 is slightly worse than B1, because funs for aitional public investment in eucation come from a reuction in public transfers to private sector (pensions etc.) rather than a reuction in public consumption. Therefore, in scenario B2, 33

34 isposable income of private sector, as well as its savings an investment are negatively affecte. inally, scenario 1 is worse than 2, because in scenario 1 extra savings of private sector (by assumption equal to 1 pp of GP) are spent primarily on investments in physical capital (97%), an only 3% are investe in eucation, whereas in scenario 2 all extra savings are investe in eucation. If follows that, given current conitions in Polan, it is much better to invest aitional savings into eucation rather than into physical capital. 8. The optimal structure of private investment Recall that represents the share of private savings evote to eucation, an it has been very low in Polan in the baseline scenario it is a mere 3.1%. As previous section implies that eucation is of crucial importance for growth, using the baseline scenario as a benchmark, we have calculate the BGR for any value of ranging from 0 to 80%. (igher values imply negative BGR, because investment in prouctive capital is so low that it oes not compensate epreciation.) igure 9 presents the results. Note that the BGR reaches maximum equal to 3.85% at 15%. Therefore, househols in Polan clearly spen too little on eucation. owever, as we argue earlier, official statistics regaring private eucation expenitures may well unerestimate the true numbers, as large part of private spening relate to eucation is classifie as consumption). Thus it s har to provie precise conclusions on that matter. 34