In 1500, Italy was by far the richest country in Europe. However, the Italian economy completely stagnated throughout the Colonial Era. By 1700, three European countries had higher per-capita GDP, and by 1820 most countries were better off than Italy. What caused such the stagnation?

The answer can be organized along three general interlinked factors (roughly presented here in chronological order): The Italian Wars, Atlantic Trade, and the Industrial Revolution.

That war is disruptive to the economy is not a novel idea. While it's increasingly difficult to derive estimates on economic prosperity the further back in history we travel (I'm pretty sure your source is the Maddison Project estimates, so you can verify this yourself) to offer an unrelated example, after the highs of the Roman Empire it's generally accepted that the real regression in Italian economic life didn't really happen after the end of the Empire itself, but rather in the wake of the Gothic and Lombard wars a few centuries later. While the Italian Wars of the 16th century were not as damaging as the system-defining wars of the earliest medieval period, the conflict (which saw almost every major European power involved at some point) nonetheless caused a noticeable dip in per-person economic productivity which the peninsula would take a century or two to bounce back from.

The most significant impact of the Italian Wars, however, did not come in the form of direct damage to economic activity. Rather, the dedication of resources to war and subsequent reconstruction robbed Italian decision-makers of the opportunity to divert excess resources to take advantage of rapidly growing Atlantic Trade. The boom of Atlantic Trade is itself a complicated creature. The colonization of the Americas was an important factor, and while the overall impact of colonization on state coffers is ambiguous (an important thing to keep in the mind in an era of hit-and-miss state-sponsored mercantilist commerce: the maintenance of colonies is expensive, while revenue from both taxes and commerce is dependent on highly variable factors) it is undeniable that individuals involved in the process did become very wealthy indeed. These individuals could then redeploy their earnings at home, contributing to the creation of a larger and more prosperous Atlantic-facing mercantile class. The growth of an Atlantic-facing merchant class also encouraged the development of intra-Europe trade routes along the Atlantic (and North Sea). Thus even net of the wars on the peninsula, the Italian mercantile class would likely have been matched by an increasingly active and prosperous Atlantic-facing mercantile class that not only had a much higher ceiling for growth (the Atlantic is bigger than the Mediterranean) but was also catalyzing growth by innovation much faster than the Mediterranean was (the colonization process contributed to Northern Europe overtaking the Mediterranean in developing early financial instruments, larger and safer seafaring vessels, and even improving the efficiency of government institutions).

Was the Italian exclusion from Atlantic growth a foregone conclusion? Maybe yes, maybe no. Even without the war, Italians were located in weak and fragmented states (a significant drawback in an era where state-sponsored trade was the norm) far from any Atlantic harbor, and would therefore have been left trying to appropriate slices of the pie from the outside. The wars merely made this difficult situation worse: in the 15th century Italian merchants and bankers had been present in the early Atlantic trade hubs (mostly in the Low Countries - which most approached Italy in terms of Renaissance-era prosperity) but they had all reeled in their investments over the course of the wars in first half of the 16th century. And while some communities were able to claw beneficial positions (Genoese bankers were able to carve out a place for themselves in the Spanish Empire, while the Venetians maintained a small but verifiable presence in Paris, London, and the Low Countries) by and large the presence of Italians in Atlantic trade was small.

So Italian economic actors were largely (not entirely, but still significantly) cut off from Atlantic-driven growth, and condemned to centuries of maintaining the status quo. In other words, stagnation. This meant that Italy's exclusion from the early Industrial Revolution was par for the course: incomes were rising rapidly in England and the Low Countries, but remained fairly constant in Italy (almost all rapid economic growth after the turn of the 19th century is pretty much industrial growth). But here the question isn't really why the Industrial Revolution didn't happen in Italy (we could just as easily ask why industrialization didn't begin in Spain, France, or Germany, for that matter). What is more important to look at is why the Italian peninsula had such a hard time converting to an industrial economy even after other regions of Europe like France and Germany began catching up to the early industrializers (I'd hold off from saying "Most Countries" though, as Iberia, all of Eastern Europe, and pretty much the rest of the world outside the United States also had yet to industrialize).

Early industrial policy can only really do one thing: acknowledge that an economy does not have the same characteristics as Great Britain (or the Low Countries) and try to substitute missing factors by developing comparable local factors. In France, an example of a "Substitution Factor" was Public Sector investment (which did have some other drawbacks in terms of efficient allocation of resources) while in Germany, policy fostered large universal banks encouraged to collaborate closely with industry (substituting the private capital investments which instead drove industrialization in Great Britain). The issue with Italy is that the peninsula is missing a whole lot of factors critical to industrialization, foremost of which was the lack of a large unified internal market which could create demand for industrial goods to begin with. Sure, Italy unified before Germany which did go on to become a successful industrializer, but while Germany was able to rally behind the unstoppable force of Prussia (however reluctantly) in an increasingly integrated political and economic system, the Italian unification process instead needed to overcome deep divisions between opposing forces (notably the Austrian Empire, which exerted both direct and indirect control over large parts of the peninsula). Thus the Italian government spent time and resources imposing uniform institutions on the peninsula in the decades following unification, while Germany managed a unification that was much more seamless and freed up resources for a rapid economic catch-up.

Italian economic growth does creep forwards after unification, but never really takes off as it does elsewhere. There are some industrial hubs which do emerge (notably Milan, Turin, and Genoa) but the rest of the country remains largely agricultural (any pre-industrial economy is fundamentally agricultural: even the great trading hubs of the Renaissance were exceptions in the midst of an agricultural economy). Indeed, many of the old mercantile centers on the peninsula even begin declining after unification, as what capital did exist was drawn to the few parts of the country which industrialized (Venice is the usual example offered, although its material decline had actually started pre-unity, when the railhead to Trieste was completed).

A final factor to consider with regards to Italy's slow industrialization is the interest (or lack thereof) by the local capital-owning class. While there were notable industrialists in Italian history (the country's first prime minister, Camillo Benso, was a committed industrial capitalist) many capital-owning Italians were unwilling to divest from agriculture. This is the tragedy of prosperous pre-industrial economies: while large mercantile centers are always a boon to economic activity, pre-industrial prosperity is largely a function of agricultural productiveness. As Italy was (and still is) an agriculturally prosperous country, capital owners found little incentive to divest from existing agricultural activity. As these same people by and large populated the political system, this created little incentive to find a policy-driven path to industrialization (until the lead-up to the First World War would change the paradigm; somewhat similarly, France also was initially a largely agricultural country and a reluctant industrializer, however geopolitical events "frightened" the country's political leadership into finding a path to industrialization in the second half of the nineteenth century; an imperative which their Italian counterparts only perceived several decades later).

The story of Italy's modern economy is a story of stagnation until the contemporary era. Unfortunately, I've glossed over some elements, and did not touch upon the numerous institutions and regional peculiarities that characterized the Italian economy both during the Italian Wars, and in the lead-up to industrialization. I also offered a hurried summary of economic development in Atlantic-facing Europe in favor of providing a summary from the Italian perspective, an inevitable but necessary compromise (we are talking about comparative growth after all). All this to say I'll be happy to clarify any and all points.

Italy's (I'm using "Italy" to refer to the the geographic area which now constitutes the country of Italy as Italy was several hundred years away as a political entity/reality) vast wealth was mainly created and supported by its maritime trade. It's geography and location were highly advantageous in exploiting the Mediterranean Sea trade. It's political history favored a decentralization of city/regional governments instead of a strong central government which could levy wide area taxes and other revenue options which were becoming the norm for what is currently thought of as the traditional nation-state.

From it's vantage point and with it's (collective) merchant navy, Italy was in a position to service all of Europe, North Africa and the Middle East. It was in a fantastic position to exploit all the trade routes except the far east trade routes (which had to go to the middle east end then to the eastern Mediterranean ports where Italian merchants could then pick up the goods for further distribution). Their presence was so prevalent than many, if not most, of the important port cities of Europe, N. Africa and the Middle East, had Italian quarters (really Venetian/Genoese/Neapolitan quarters and districts, sometime all three).

Trade was good and trade was lucrative. The Italians had been working these routes for a few centuries by the 1500s and had developed secondary money industries such as banking and investing. It was this wealth that prompted the other European powers to look for a way to compete. Portugal sent sailors around Africa and to India/China/Spice Islands. Spain sent Columbus west where he discovered the new world in 1492.

Starting in the 1500's with routes around the New World and Africa opened up, what had been a prime position for Italy, now became a box from which they could not easily escape. Setting aside the ever present resistance to change usually exhibited by established powers, Italy now found its reach greatly shortened. Where before it could force itself as the middle man between the three continents, now all the continents could deal with each directly.

All of Italy's ships were now bound by the Mediterranean. there was no Suez canal. No outlet except through the Straight of Gibraltar which was dominated by Spain and Portugal, and later other Northern European Sea Powers, who worked hard to deny Italian ships passage. Furthermore, as these other powers were utilizing open ocean passages, it necessitated building much larger, sturdy and capable ships. These ships made great warships which could then easily handle the much lighter, traditional Italian trading vessels.

Access to the open ocean now became the key strategic point for dominating trade. Whole swaths of middle men could be excluded and Spain, Portugal and later Netherlands and England and Scandinavia cashed in. Additionally, turns out the ocean also opened routes to lots of resource rich lands which were sparsely occupied (usually thanks to European diseases) and/or occupied by societies with much less technological development. So, instead of just being limited to utilizing trade routes, these countries now were able to utilize their new found strength as unified nation states to create colonies. So, they obtained their trade goods literally at wholesale prices and could then directly deliver them to any markets they want to maximize selling prices.

Italy simply could not compete. Without the huge influx of trade profit, it fell behind the countries able to exploit colonization and trade.

EDITED the text to expel Bonaparte from Naples and replace Milan with Genoa.