The Interaction and Sequencing of Policy Reforms

Transcription

1 The Interaction and Sequencing of Policy Reforms Jose Asturias School of Foreign Service in Qatar, Georgetown University Sewon Hur University of Pittsburgh Timothy J. Kehoe University of Minnesota, Federal Reserve Bank of Minneapolis, and National Bureau of Economic Research Kim J. Ruhl Stern School of Business, New York University University of Pittsburgh October /57

2 Which reforms? When? Countries face broad array of potential reforms IMF Title IV consultation for Brazil (May 2015) relatively closed economy tax system is uncommonly complex high risk loans by public banks How do reforms interact? Suppose we are forced to do reforms sequentially. Does the order matter? 2/57

3 Model of sequencing of reforms We construct a two country, general equilibrium model in which economic growth is driven by continual entry of more productive firms. Firms in model face three policy barriers: Cost of creating new firm Trade cost Contract enforcement (banking efficiency). Easy to characterize balanced growth path. 3/57

4 Numerical experiments Calibrate symmetric two country model in which the United States trades with the rest of the world. Simulate 6 different sequences of reforms that are symmetric and multilateral. Economy starts in distorted balanced growth path in year 0. Unexpected reform 1 in year 1. Afterwards, perfectly foreseen reform 2 in year 5 and reform 3 in year 9. 4/57

5 Findings Best reform sequence involves reforming trade cost first. Worst reform sequence involves reforming enforcement of contracts first. Large welfare differences: 4.8 percent of year 1 consumption to compensate worst sequence. 5/57

6 Intuition Trade reform induces: less productive potential firms to not enter productive domestic firms to export. Enforcement reform induces: less productive potential firms to enter productive domestic firms to export, but pay high trade cost. 6/57

7 Model Two countries, 1 and 2. Continuum of tradable intermediate good firms monopolistic competitors fixed cost to create firm, fixed cost to export endogenous borrowing constraints. Representative final good producer aggregates intermediate goods. 7/57

8 Households Representative household in country i solves s.t. maxå t b logc t= 0 it itcit + it+ 1 it+ 1= it i + Dit + Bit D i0, B i0 given P q B w L where D it = dividends from domestic firms. 8/57

9 Final good producers Perfect competition, constant returns to scale. d e Purchase intermediate goods ( y, y ) to solve min p ( w) y ( w) dw+ p ( w) y ( w) dw ò wîw d it d d ò e e it it e jt jt wîw it 1 d r r r w w+ ò e it w w e jt it wîw æ ö s.t. ç = çèò y ( ) d y ( ) d wîw Y. d it jt ø d W it: country i s domestic varieties. e W jt: country j s exported varieties to country i. 1 1-r : elasticity of substitution for 0< r < 1. jt jt 9/57

10 Intermediate goods producers Measure m i of potential entrants each period. Potential entrants draw from productivity distribution -g æ ö x F = - it( x) 1 for x³ xg i ç t èxg ø i where the mean of distribution grows at rate g -1. Production technology of firm w y ( w) = x ( w) ( w). it it it t 10/57

11 Fixed costs Firms face two fixed costs d k i in units of domestic labor k e i in units of foreign labor, where k e i > k. d i Time to build constraint: One period gestation lag after paying fixed cost before operation begins. 11/57

12 Prices Existing firm chooses price to maximize profits in domestic market d d d d yit( w) pit ( w) = max pit( w) yit( w) - wit x ( w) Existing firm chooses price to maximize profits in export market it e e e p ( w) = max p ( w) y ( w) - w it it it it y x e it it ( w) ( w) 12/57

13 Prices Constant markup pricing for both domestic and export markets p w ( w) = pit( w) = rx ( w). d e it it it Pricing decisions can be re written as a function of d e productivity p ( x) = p ( x). it d e Profitability re written as p () x and p () x. it it it 13/57

14 Existing exporter Exporter has state vector ( bx,) and chooses debt, dividends, and exit decision to solve e e Vit (,) b x = max éd+ qit+ 1( 1-d) Vit+ 1( b',) x,0ù ë û d e s.t. d= p () x + p () x + ( 1- d ) q + 1b' - b³ 0 it it it ( q ) e e V (,) b x ³ 1 - V (0,) x. it i it Once a firm exits, there is zero exit value and it cannot re enter. Firms die with probability d each period. 14/57

15 Limited enforcement of contracts Degree of enforceability of contracts governed by q i. Manager of a firm can abscond with fraction ( 1-qi ) of the value of the firm in case of default. Enforcement constraint implies that manager s value of honoring debt is greater than that of absconding ( ) e e V ( b, x) ³ 1 -q V (0, x ). it i it Possible range: 1³ q > 0 i. 15/57

16 Existing non exporter Non exporter has state vector ( bx,) and chooses debt, dividends, and export/exit decision to solve V n it é n n d + q + ( d) ù it Vit+ 1( b', x), (,) b x = max e e + + ( -d êë d qit 1 1 ) Vit+ 1( b', x),0ú û n d s.t. d = pi t() x + ( 1 - d ) qit+ 1b' -b³ 0 ( ) qit 1b ( q ) e d e d = p ( x) + 1- d + '-b-w k ³ 0 it n n V (,) b x ³ 1 - V (0,) x. it i it jt i If a firm chooses to become an exporter, it pays fixed e cost w k but it does not export until next period. jt i 16/57

17 Potential entrant s decision to enter domestic market Potential entrant pays fixed cost w only if: k d it i value of firm is greater than zero æ d k ö n ç w V, x 0., it+ 1 it i ç( - ) è 1 q ø ³ d it+ 1 there exists a debt path such that all enforcement constraints are satisfied. Solution characterized by cutoff productivities x ˆd i0t : potential entrant productivity needed to enter. x ˆd ikt: minimum productivity of firms, age k at time t. 17/57

18 Potential entrant s decision to enter export market Potential entrant pays fixed cost market and k d it i w k to enter export w to enter domestic market only if: value of entering both markets is greater than the value of only entering the domestic market V æ d e k k ö æ d k ö wit i + wjt i, ç ( d) ç( d) è - ø ³ n wit i x V è - ø ³ it 1, x 0, 1 q 1 q e it+ 1 + it+ 1 it+ 1 there exists a debt path such that all enforcement constraints are satisfied. Solution characterized by cutoff productivities. jt e i 18/57

19 Export cutoff productivities x ˆe ik t: minimum productivity of firms of age k who pay the export cost at age. x ˆe ikt: minimum productivity of exporting firms, age k at time t. 19/57

20 Measure of exporting firms Measure of exporting firms h e it evolves according to ( )( ) h e + = h e 1 + l e 1-d it it it. Measure of new exporters l e it = m é ( e - ) ù+ m -d é ( ) ( ) ù ê ú å ˆ 1 ˆ n 00 = ê ë û it k e e (1 ) ˆ ˆ i Fit xi t 1 i Fit k xikt Fit k x ikkt ë ú. k û new entrant exporters new exporters, age k n ˆit : oldest age at which a firm born in period t pays the export cost. 20/57

21 Measure of domestic firms Measure of domestic firms h d it evolves according to Measure of new firms l d ( )( ) h d + = h d 1 + l d 1-d it it it. it ( d 1 ˆ ) d l = m( - ) it i it i0t F x. 21/57

22 Definition of equilibrium Given initial conditions, an equilibrium is sequences for i = 1,2 of prices { wit, Pit, q it + 1} t = 0 aggregate income, consumption, dividends, and bonds entry thresholds new entry measures prices and allocations for intermediate firms that produce for the domestic and export market 22/57

23 such that in both countries household maximizes lifetime utility, intermediate good firm maximizes discounted dividends and entry exit thresholds solve entry exit problem, final good firm minimizes cost and earns zero profits, clearing conditions: labor market, bond market, dividend payments, balanced trade. 23/57

24 Proposition 1. Balanced growth path exists Equilibria converge to a balanced growth path in which aggregate income, consumption, dividends, and bonds grow by g, entry and exit thresholds grow by g, measures of entrants and firms remain constant. 24/57

25 Balanced growth path (BGP) We prove the existence of a balanced growth path and characterize key variables. In the characterizations of BGP q <1 i so enforcement is imperfect, k d i is low enough relative to k e i so that the marginal entrant never exports, 1(1 - r) > 2 so that profits of a firm decrease over time. 25/57

26 Domestic cutoffs for cohort aged 0 Enforcement constraint at age 1 holds with equality for the domestic marginal entrant. Enforcement constraints for this firm do not hold with equality after age 1. It is most advantageous to default at age 1 because debt is highest; declining profitability through time implies that age 1 is when the value of the firm is highest. 26/57

27 Expression for domestic cutoff for cohort aged 0 Enforcement constraint holds with equality for the cutoff firm at age 1: 1-r 1-r æ ö r d d d r = k k q 1 wit 1 i0t i( i i ç è1-r wit Y it ø r x ˆ, ). Similar to condition in static model except that the entry cost in that expression is replaced with effective entry cost k d i. 27/57

28 How is k d i related to policy variables? d d d i i i, q) = k ( k i å m= 1 k ( 1- ) m q d b m g -r m 1-r If k d i increases or q i declines, k d i increases. As q i approaches 0, k d i approaches infinity since firms can no longer finance the entry cost. 28/57

29 Debt, profits, and dividends of a domestic firm 29/57

30 Condition for export cutoffs For a firm that pays w at age, EC at age + 1 either e jt i b holds with equality for the cutoff exporting firm or is slack, in which case, determined by ( ( ) ) n = ( ) ( ) k t V b xˆ, xˆ V b xˆ, x ˆ e e e e d e e i, + 1, t-++ k 1 i,, t-++ k 1 ik t ik t i, + 1, t-++ k 1 i,, t-++ k 1 ik t i where e i,, t-++ k 1 d i,, t-++ k 1 : debt chosen at age after paying trade cost, b : debt chosen at age. 30/57

31 Expression for constrained marginal exporter Condition that enforcement constraint at age + 1 holds with equality for the cutoff exporting firm: 1-r 1- r æ ö r ec ec k ( d e d e k k q k k q ) r 1 wit- k 1 wit- k = ik t i 1, 1, 1, 2, 2 2 ç è1-r P it-kyit -k ø r Pit- k xˆ, As before, expression is similar to the static case except that the entry cost is replaced with k ec i. 31/57

32 How is k ec i related to policy variables? ( 1, 1, 1, 2, 2, 2) k k k q k k q ec d e d e i = ( 1 ) w e d i d b ki + ki D - é ù q ú d b d b ëê úû -1 -r -r 1 m m m Y P -r m 1-r m ê m 1-r 1+D D úå ( 1- ) g + ( 1- ) g i i i m=+ 1 å m = 1 If either fixed costs (k d i or k e i ) increase or q i declines then k ec i increases. As q i approaches 0, k ec i does not approach infinity since firms can self finance trade cost. k ec i is decreasing in : As firms pay down existing debt, EC becomes less binding. 32/57

33 Unconstrained marginal exporter e Using ( e ) n, ˆ = ( e, ) V x V x, we find ˆ i, + 1, t-++ k 1 ik t i, + 1, t-++ k 1 ik t 1-r 1- r æ ö r eu( d e d e k k q k k q ) r 1 wit- k 1 wit- k i 1, 1, 1 2, 2, 2 ç è1-r P it-kyit -k ø r Pit- k eu xˆ = k, ik t As before, expression is similar to the static case except that the entry cost is replaced with k eu i 33/57

34 How is k eu i related to policy variables? ( 1, 1, 1, 2,, ) k k k q k k q eu d e d i r w e 1-r e Di ki g 2 2 = -1 -r m Y P1-r m m 1-r DD i i å ( 1-d) b g m= 1 If k e i increases, then k eu i increases is increasing in : the more a firm waits to pay eu ki the export cost, the more profitable it needs to be. In general, the marginal exporter efficiency is { } xˆ = max xˆ, x ˆ e ec eu ik t ik t ik t 34/57

35 How does enforcement affect export cutoffs? With perfect enforcement, any firm that will ever export pays the fixed cost at age 0 and cutoff is x ˆe i,0,0, As enforcement worsens, less efficient firms take longer to export because they must first decrease their debt, cutoffs for cohort aged 0 at time t : e e e xˆ > ˆ,0,0,,0,1, > > ˆ i t xi t... x i,0, nˆ, it t e e e i i i it Pay k age 0 Pay k age 1 Pay k age nˆ t 35/57

36 Debt, profits, and dividends of an eventual exporter 36/57

37 Numerical experiment Calibrate the model to the U.S. economy trading with a symmetric economy, which represents the rest of the world. Examine welfare implications of symmetric multilateral reforms. 37/57

38 Calibration parameter value target / source fixed cost domestic fixed cost export d k 8.6 average U.S. establishment size: 16.0 e k enforcement q fraction of exporting firms: 21.0 percent debt / revenue of firms of age less than 5: 0.27 Pareto parameter g 4.04 std. dev. of U.S. establishment size: 91.2 death rate d 0.10 establishment death rate: 10 percent per year discount factor b 0.98 real interest rate: 4 percent per year entrant productivity growth g 1.02 BGP growth factor: 1.02 per year 38/57

39 Numerical experiment Starting from the U.S., we solve for three separate distorted economies each with income levels that are three percent lower than the U.S. In these three economies Entry cost increases from 8.6 to Enforcement decreases from 0.39 to Trade cost increases from 40.9 to /57

40 Numerical experiment We begin with an economy with all 3 distortions. We consider transition paths of 6 possible reforms sequences that converge to balanced growth path with no distortions. Each sequence involves first unanticipated reform followed by second and third anticipated reforms 4 years apart. 40/57

41 Comparing balanced growth paths Changes in income levels one reform reform output gain (percent) trade cost 3.71 entry cost 3.44 enforcement 3.17 Trade reform delivers the highest income level as the first reform. 41/57

42 Interaction of reforms reform #1 reform #2 trade cost entry cost substitutable trade cost enforcement substitutable enforcement entry cost complementary Substitutable: once a country has enacted one reform, the percentage increase in GDP from enacting the other reform decreases. Complementary: once a country has enacted one reform, the percentage increase in GDP from enacting the other reform increases. 42/57

43 Varieties available to consumers The total varieties available to consumers are NE E E V = D + D + F. total varieties domestic non exporting domestic exporting foreign exporting We decompose the percentage change in varieties into the corresponding components NE E E DV DD DD DF = + + V V V V. 43/57

44 Decomposing changes in varieties reform varieties available to consumer domestic non exporting firms domestic exporting firms foreign exporting firms percent change enforcement entry cost trade cost Reforms to entry costs and enforcement increase varieties and non export firms, but crowd out exporting firms. 44/57

45 Crowding out of export firms Two opposing effects: Direct: effective entry cost of exporting declines if q increases or d k declines. General equilibrium: increase in number of firms raises wages and reduces the profitability of exporting. General equilibrium effect is stronger. 45/57

46 Welfare effects with transition dynamics Consider welfare effects of all possible sequences with 1 reform, 2 reforms, 3 reforms. 46/57

47 Welfare gains from 1 reform reform real income (100 = no reform) entry cost trade cost enforcement Entry cost reform yields highest welfare gain. Trade reform results in the highest balanced growth path consumption level, but less beneficial. 47/57

48 Detrended consumption paths Consumption path with trade reform has large drop. Entry cost reform preferred even though it has a lower balanced growth path consumption level. 48/57

49 Welfare gains from 2 reforms reform #1 reform #2 real income (100 = no reform) entry cost enforcement enforcement entry cost trade cost entry cost entry cost trade cost trade cost enforcement enforcement trade cost Best sequences involve entry cost and enforcement reforms, which are complementary. Trade reform is substitutable with other reforms and has large initial drop in consumption. 49/57

50 Detrended consumption paths Trade reform no longer delivers higher BGP consumption: substitutable with other reforms. It also has large initial drop in consumption. 50/57

51 Welfare gains from 3 reforms reform #1 reform #2 reform #3 real income (100 = no reform) trade cost enforcement entry cost trade cost entry cost enforcement entry cost enforcement trade cost entry cost trade cost enforcement enforcement entry cost trade cost enforcement trade cost entry cost Best sequences involve reforming trade cost first. Worst sequences involve reforming enforcement first. 51/57

52 Welfare gains from 3 reforms reform #1 reform #2 reform #3 real income (100 = no reform) trade cost enforcement entry cost trade cost entry cost enforcement entry cost enforcement trade cost entry cost trade cost enforcement enforcement entry cost trade cost enforcement trade cost entry cost Welfare differences are large: 0.1 percent permanent real income, equivalent to 4.8 percent of period 1 consumption to compensate worst sequence. 52/57

53 Compare best and worst reform sequence We compare the transition path for the most and least beneficial reform sequence best: trade cost, enforcement, entry cost worst: enforcement, trade cost, entry cost We find reducing trade reform increases the mass of exporters and reduces the mass of domestic only firms. We find enforcement reform increases the mass of domestic only firms. 53/57

54 Detrended consumption Initial drop in consumption after trade reform, but consistently higher consumption afterwards. 54/57

55 Mass of exporters Trade cost reform leads to increase in the mass of exporters. Differences in timing of trade reform leads to large and persistent differences in the mass of exporters. 55/57

56 Mass of domestic only firms Trade reform decreases the mass of unproductive domestic only firms. Enforcement reform increases the mass of unproductive domestic only firms. 56/57

57 Conclusion We construct and calibrate a model with three potential reforms that a government can undertake. We find that the order in which reforms are implemented matters and that the best reforms are those that reduce trade costs first. The timing of reforms can lead to welfare differences of 0.1 percent in life time consumption, equivalent to 4.8 percent of year 1 consumption. 57/57